US20240027317A1 - Measuring density of multiphase fluids - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N9/00—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity
- G01N9/26—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity by measuring pressure differences
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
- G01F1/74—Devices for measuring flow of a fluid or flow of a fluent solid material in suspension in another fluid
Definitions
- This disclosure relates to characterization of the flow of multiphase fluids.
- a multiphase fluid is a mixture of multiple phases of matter.
- Multiphase fluids can be non-homogenous and can thus exhibit complex flow characteristics.
- the characteristics of the flow of multiphase fluids in a conduit can depend on various factors, such as operating conditions (pressure and temperature), composition (and in turn, physical properties such as density and viscosity) of each of the phases, flow rate of each of the phases, and physical characteristics of the conduit (such as diameter and orientation) through which the multiphase fluid is flowing. Characterization of the flow of multiphase fluids can sometimes be difficult. In some cases, for example, in oil and gas operations, accurate flow metering of multiphase fluid mixtures (such as crude oil, natural gas, and brine) can be important.
- the system includes a U-bend, a first differential pressure sensor, a second differential pressure sensor, and a computer.
- the U-bend is configured to flow a multiphase fluid.
- the U-bend includes a first conduit, a second conduit, and a connecting conduit.
- the connecting conduit connects the first conduit to the second conduit.
- Each of the first conduit and the second conduit have substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend.
- the multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit.
- the multiphase fluid includes a gas phase, an aqueous phase, and an oil phase.
- the first differential pressure sensor is coupled to the first conduit.
- the first differential pressure sensor is configured to measure a first differential pressure of the multiphase fluid flowing through the U-bend across a specified differential pressure height along the first conduit.
- the second differential pressure is coupled to the second conduit.
- the second differential pressure sensor is configured to measure a second differential pressure of the multiphase fluid flowing through the U-bend across the specified differential pressure height along the second conduit.
- the computer includes a processor and a computer-readable storage medium.
- the processor is communicatively coupled to the first differential pressure sensor and to the second differential pressure sensor.
- the computer-readable storage medium is coupled to the processor and stores programming instructions for execution by the processor.
- the programming instructions instruct the processor to perform operations.
- the operations include receiving a first differential pressure signal from the first differential pressure sensor.
- the first differential pressure signal represents the first differential pressure of the multiphase fluid.
- the operations include receiving a second differential pressure signal from the second differential pressure sensor.
- the second differential pressure signal represents the second differential pressure of the multiphase fluid.
- the operations include determining a mixture density of the multiphase fluid at least based on the specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid.
- the mixture density of the multiphase fluid is determined by:
- ⁇ ⁇ ⁇ P 1 - ⁇ ⁇ P 2 2 ⁇ g ⁇ h ,
- ⁇ is the mixture density of the multiphase fluid
- ⁇ P 1 is the first differential pressure of the multiphase fluid
- ⁇ P 2 is the second differential pressure of the multiphase fluid
- g is an acceleration due to gravity
- h is the specified differential pressure height.
- the operations performed by the processor include determining a total mass flow rate of the multiphase fluid by:
- m T is the total mass flow rate of the multiphase fluid
- C d is a discharge coefficient
- ⁇ is an expansion factor
- K is a fixed geometry factor related to a cross-sectional flow area of the U-bend
- ⁇ is the mixture density of the multiphase fluid
- ⁇ P is the first differential pressure or the second differential pressure of the multiphase fluid
- k f is a geometry-based correction factor for friction
- ⁇ P f is frictional pressure loss.
- the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit.
- the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.
- the connecting conduit is perpendicular to the first conduit and to the second conduit.
- the operations performed by the processor include receiving, as input, a gas phase volume fraction of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, a gas phase density of a gas phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an aqueous phase density of an aqueous phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an oil phase density of an oil phase of the multiphase fluid. In some implementations, the operations performed by the processor include determining an aqueous phase volume fraction of the multiphase fluid by:
- ⁇ is the mixture density of the multiphase fluid
- ⁇ g is the gas phase volume fraction of the multiphase fluid
- ⁇ ⁇ is the aqueous phase volume fraction of the multiphase fluid
- ⁇ g is the gas phase density of the gas phase of the multiphase fluid
- ⁇ a is the aqueous phase density of the aqueous phase of the multiphase fluid
- ⁇ o is the oil phase density of the oil phase of the multiphase fluid.
- the operations performed by the processor include receiving, as input, an aqueous phase volume fraction of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, a gas phase density of a gas phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an aqueous phase density of an aqueous phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an oil phase density of an oil phase of the multiphase fluid. In some implementations, the operations performed by the processor include determining a gas phase volume fraction of the multiphase fluid by:
- ⁇ is the mixture density of the multiphase fluid
- ⁇ g is the gas phase volume fraction of the multiphase fluid
- ⁇ a is the aqueous phase volume fraction of the multiphase fluid
- ⁇ g is the gas phase density of the gas phase of the multiphase fluid
- ⁇ a is the aqueous phase density of the aqueous phase of the multiphase fluid
- ⁇ o is the oil phase density of the oil phase of the multiphase fluid.
- a multiphase fluid is flowed through a U-bend.
- the multiphase fluid includes a gas phase, an aqueous phase, and an oil phase.
- the U-bend includes a first conduit, a second conduit, and a connecting conduit.
- the connecting conduit connects the first conduit to the second conduit.
- Each of the first conduit and the second conduit have substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend.
- the multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit.
- a first differential pressure of the multiphase fluid is measured across a specified differential pressure height along the first conduit.
- a second differential pressure of the multiphase fluid is measured across the specified differential pressure height along the second conduit.
- a mixture density of the multiphase fluid is determined at least based on the specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid.
- the mixture density of the multiphase fluid is determined by:
- ⁇ ⁇ ⁇ P 1 - ⁇ ⁇ P 2 2 ⁇ g ⁇ h ,
- ⁇ is the mixture density of the multiphase fluid
- ⁇ P 1 is the first differential pressure of the multiphase fluid
- ⁇ P 2 is the second differential pressure of the multiphase fluid
- g is an acceleration due to gravity
- h is the specified differential pressure height.
- a total mass flow rate of the multiphase fluid is determined by:
- m T is the total mass flow rate of the multiphase fluid
- C d is a discharge coefficient
- ⁇ is an expansion factor
- K is a fixed geometry factor related to a cross-sectional flow area of the U-bend
- ⁇ is the mixture density of the multiphase fluid
- ⁇ P is the first differential pressure or the second differential pressure of the multiphase fluid
- k f is a geometry-based correction factor for friction
- ⁇ P f is frictional pressure loss.
- an aqueous phase volume fraction of the multiphase fluid is determined by:
- ⁇ is the mixture density of the multiphase fluid
- ⁇ g is a gas phase volume fraction of the multiphase fluid
- ⁇ a is an aqueous phase volume fraction of the multiphase fluid
- ⁇ g is a gas phase density of the gas phase of the multiphase fluid
- ⁇ a is an aqueous phase density of the aqueous phase of the multiphase fluid
- ⁇ o is an oil phase density of the oil phase of the multiphase fluid.
- a gas phase volume fraction of the multiphase fluid is determined by:
- ⁇ is the mixture density of the multiphase fluid
- ⁇ g is a gas phase volume fraction of the multiphase fluid
- ⁇ a is an aqueous phase volume fraction of the multiphase fluid
- ⁇ g is a gas phase density of the gas phase of the multiphase fluid
- ⁇ a is an aqueous phase density of the aqueous phase of the multiphase fluid
- ⁇ o is an oil phase density of the oil phase of the multiphase fluid.
- the first differential pressure of the multiphase fluid is measured by a first differential pressure sensor coupled to the first conduit.
- the second differential pressure of the multiphase fluid is measured by a second differential pressure sensor coupled to the second conduit.
- the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit.
- the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.
- FIG. 1 A is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid.
- FIG. 1 B is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid.
- FIG. 1 C is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid.
- FIG. 1 D is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid.
- FIG. 1 E is a schematic diagram of an example apparatus which can be used to measure a flow rate of a multiphase fluid.
- FIG. 1 F is a schematic diagram of an example apparatus which can be used to measure a flow rate of a multiphase fluid.
- FIG. 1 G is a schematic diagram of an example apparatus which can be used to measure a water-liquid ratio of a multiphase fluid.
- FIG. 1 H is a schematic diagram of an example apparatus which can be used to measure a density and a flow rate of a multiphase fluid.
- FIG. 1 I is a schematic diagram of an example apparatus which can be used to measure a density, a flow rate, and a water-liquid ratio of a multiphase fluid.
- FIG. 1 J is a schematic diagram of an example apparatus which can be used to measure a density, a flow rate, and a water-liquid ratio of a multiphase fluid.
- FIG. 2 A is a schematic diagram depicting various example pressure tap arrangements.
- FIG. 2 B is a schematic diagram depicting various example piping arrangements.
- FIG. 2 C is a schematic diagram depicting various example piping arrangements.
- FIG. 2 D is a schematic diagram depicting various example piping arrangements.
- FIG. 2 E is a schematic diagram depicting various example piping arrangements.
- FIG. 2 F is a schematic diagram depicting various example sensor arrangements.
- FIG. 3 A is a flowchart depicting an example multiphase fluid flow model.
- FIG. 3 B is a flowchart depicting an example multiphase fluid flow model for determining density.
- FIG. 3 C is a flowchart depicting an example multiphase fluid flow model for determining density.
- FIG. 3 D is a flowchart depicting an example multiphase fluid flow model for determining density.
- FIG. 3 E is a flowchart depicting an example multiphase fluid flow model for determining flow rate.
- FIG. 3 F is a flowchart depicting an example multiphase fluid flow model.
- FIG. 3 G is a flowchart depicting an example multiphase fluid flow model.
- FIG. 4 is a flowchart of an example method for measuring a density of a multiphase fluid.
- FIG. 5 is a flowchart of an example method for measuring a flow rate of a multiphase fluid.
- FIG. 6 is a flowchart of an example method for measuring a density and a flow rate of a multiphase fluid.
- FIG. 7 is a block diagram of an example computer system.
- the apparatuses described here can be used to accurately measure the mixture density of multiphase fluids. The mixture density can then be used to determine other properties of the multiphase fluid, for example, based on additional known information.
- the apparatuses include multiple connected conduits including an elbow (or L-bend) and a U-bend.
- the apparatuses include multiple pressure sensors for measuring differential pressures across various location pairs of the flowing multiphase fluid. The measured differential pressures can be compared and manipulated to determine the mixture density of the flowing multiphase fluid.
- the subject matter described in this disclosure can be implemented in particular implementations, so as to realize one or more of the following advantages.
- the apparatuses, systems, and methods described here can be implemented independent of the use of radioactive energy sources (such as gamma-ray attenuation), which can be hazardous.
- the apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, even in situations in which a gas phase is present in a non-negligible amount.
- the apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, while taking into account frictional and shear pressure losses of the multiphase fluid.
- the apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, even in complex flow regimes such as slug-flow, plug-flow, and annular flow regimes.
- the apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, even in situations in which there is slip (that is, differential flow velocity) between gas and liquid phases.
- the apparatuses, systems, and methods described here can take advantage of pipe geometry (and associated fluid dynamics) to measure a relatively simple (and more direct) flow/fluid property (such as differential pressure), rather than a relatively complex (and more indirect) fluid/flow property (such as electromagnetic (spectral) absorption/transmission) to accurately determine the mixture density of a multiphase fluid.
- the apparatuses, systems, and methods described here can be implemented in conjunction with other flow metering components to supplement and/or enhance the accuracy of the characterization of multiphase fluid flow.
- FIG. 1 A depicts an apparatus 100 A which can be used to measure a density of a multiphase fluid 101 .
- the multiphase fluid 101 can be a 2-phase or a 3-phase fluid.
- the multiphase fluid 101 can include a gas phase 101 a and a liquid phase 101 b .
- the liquid phase 101 b includes an aqueous phase 101 b ′ and an oil phase 101 b ′′.
- the multiphase fluid 101 can include a gas phase 101 a , an aqueous phase 101 b ′, and an oil phase 101 b ′′.
- the multiphase fluid 101 can include hydrocarbon gas, hydrocarbon liquid, and water (or brine).
- the apparatus 100 A includes a U-bend 102 which is configured to flow the multiphase fluid 101 .
- the U-bend 102 includes a first conduit 102 a , a second conduit 102 b , and a connecting conduit 102 c .
- the second conduit 102 b is parallel to the first conduit 102 a .
- a longitudinal length of the first conduit 102 a is substantially the same as a longitudinal length of the second conduit 102 b
- a cross-sectional area of the first conduit 102 a is substantially the same as a cross-sectional area of the second conduit 102 b
- a frictional component of the pressure drop experienced by the multiphase fluid 101 flowing through these components ( 102 a , 102 b ) of the U-bend 102 is substantially the same for each component.
- each of the first conduit 102 a and the second conduit 102 b have substantially the same inner diameter, d.
- the connecting conduit 102 c connects the first conduit 102 a to the second conduit 102 b .
- the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102 .
- the connecting conduit 102 c is perpendicular to the first conduit 102 a and to the second conduit 102 b . The multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102 a , through the connecting conduit 102 c , and out of the second conduit 102 b .
- each of the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c are made of the same material, such that the friction experienced by the multiphase fluid 101 flowing through each of the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c is substantially the same.
- the connecting conduit 102 b is connected to the first conduit 102 a by a first curved bend 103 a .
- the connecting conduit 102 c is connected to the second conduit 102 b by a second curved bend 103 b .
- the first conduit 102 a , the second conduit 102 b , the connecting conduit 102 c , the first curved bend 103 a , and the second curved bend 103 b are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102 .
- the first curved bend 103 a and the second curved bend 103 b can be made of the same material as the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c , such that the friction experienced by the multiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same.
- the apparatus 100 A includes a first pair of pressure sensors 104 a , 104 b .
- the pressure sensors 104 a , 104 b are coupled to the first conduit 102 a via pressure ports 105 a , 105 b , respectively.
- the pressure sensors 104 a , 104 b are cooperatively configured to measure a first differential pressure of the multiphase fluid 101 flowing through the U-bend 102 .
- the pressure ports 105 a , 105 b to which the pressure sensors 104 a , 104 b are coupled, respectively, are separated by a specified differential pressure height, h, along the first tubular 102 a .
- the apparatus 100 A includes a second pair of pressure sensors 104 c , 104 d .
- the pressure sensors 104 c , 104 d are coupled to the second conduit 102 b via pressure ports 105 c , 105 d .
- the pressure sensors 104 c , 104 d are cooperatively configured to measure a second differential pressure of the multiphase fluid 101 flowing through the U-bend 102 .
- the pressure ports 105 c , 105 d to which the pressure sensors 104 c , 104 d are coupled, respectively, are separated by the same specified differential pressure height, h, along the second tubular 102 b .
- the height difference between the pressure ports 105 a , 105 b of the pressure sensors 104 a , 104 b and the height difference between the pressure ports 105 c , 105 d of the pressure sensors 104 c , 104 d are the same, such that the frictional components of the pressure drops experienced by the multiphase fluid 101 flowing through the first conduit 102 a (measured by pressure sensors 104 a , 104 b ) and through the second conduit 102 b (measured by the pressure sensors 104 c , 104 d ) are substantially the same.
- the first pair of pressure sensors 104 a , 104 b is replaced by a first differential pressure sensor that is coupled to the first conduit 102 a via the pressure ports 105 a , 105 b .
- the second pair of pressure sensors 104 c , 104 d is replaced by a second differential pressure sensor that is coupled to the second conduit 102 b via the pressure ports 105 c , 105 d.
- the U-bend 102 can be connected to a flow pipe 150 that flows the multiphase fluid 101 .
- the flow pipe 150 includes a first pipe 150 a and a second pipe 150 b .
- the terms “pipe” and “conduit” are synonymous.
- the term “pipe” is being used in relation to the flow pipe 150 and the term “conduit” is being used in relation to the U-bend 102 simply for consistency/clarity and to avoid confusion.
- the U-bend 102 is connected to the flow pipe 150 by angled bends 153 a , 153 b .
- the first conduit 102 a of the U-bend 102 is connected to the first pipe 150 a of the flow pipe 150 by the first angled bend 153 a .
- the second conduit 102 b of the U-bend 102 is connected to the second pipe 150 b of the flow pipe 150 by the second angled bend 153 b .
- the angled bends 153 a , 153 b are 90-degree angled bends.
- the angled bends 153 a , 153 b can have a different degree angle, such as in a range of from 30 degrees to 150 degrees.
- the first conduit 102 a , the second conduit 102 b , the connecting conduit 102 c , the first curved bend 103 a , the second curved bend 103 b , the first angled bend 153 a , the second angled bend 153 b , and the flow pipe 150 are integrated, such that the U-bend 102 and the flow pipe 150 form a singular, unitary body, as opposed to parts that are disjointed and coupled together.
- the angled bends 153 a , 153 b are replaced by curved bends (similar to the curved bends 103 a , 103 b ).
- the inner diameters (d) of the first conduit 102 a and the second conduit 102 b are different from the inner diameter (D) of the flow pipe 150 .
- a change in cross-sectional flow area between the flow pipe 150 and the U-bend 102 can ensure that the differential pressures of the multiphase fluid 101 flowing across the angled bends 153 a , 153 b are predominantly functions of the total flow rate of the multiphase fluid 101 as opposed to other factors, such as frictional pressure losses.
- the inner diameters (d) of the first conduit 102 a and the second conduit 102 b can be in a range of from half of the inner diameter (D) of the flow pipe 150 to double the inner diameter (2D) of the flow pipe 150 (that is, D/2 ⁇ d ⁇ 2D).
- each of the pressure sensors are at least a threshold distance away from the closest bend.
- the threshold distance is long enough to allow the flow of the multiphase fluid 101 to fully develop after the disturbance in flow caused by an upstream bend or long enough to allow the flow of the multiphase fluid 101 to remain fully developed before approaching a downstream bend.
- the method of sensing can determine the location at which the sensors should be placed.
- the threshold distance can be, for example, four times the inner diameter, d (that is, 4d).
- the threshold distance is 4 inches.
- the pressure port 105 a to which the pressure sensor 104 a is coupled, is located on the first conduit 102 a at least 4d distance away from the angled bend 153 a .
- the pressure port 105 b to which the pressure sensor 104 b is coupled, is located on the first conduit 102 a at least 4d distance away from the curved bend 103 a .
- the pressure port 105 c to which the pressure sensor 104 c is coupled, is located on the second conduit 102 b at least 4d distance away from the curved bend 103 b .
- the pressure port 105 d to which the pressure sensor 104 d is coupled, is located on the second conduit 102 b at least 4d distance away from the angled bend 153 b.
- the apparatus 100 A can be communicatively coupled to a computer 700 .
- the computer 700 includes a processor 705 and a memory 707 .
- the processor 705 can be communicatively coupled to the first pair of pressure sensors 104 a , 104 b (or first differential pressure sensor) and to the second pair of pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the memory 707 is coupled to the processor 705 .
- the computer 700 is also shown in FIG. 7 and is described in more detail later.
- the memory 707 stores programming instructions for execution by the processor 705 .
- the programming instructions can instruct the processor 705 to perform various operations.
- the operations performed by the processor 705 can include receiving a first differential pressure signal from the first pair of pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the first differential pressure signal can represent the first differential pressure of the multiphase fluid 101 measured by the first pair of pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the operations performed by the processor 705 can include receiving a second differential pressure signal from the second pair of pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the second differential pressure signal can represent the second differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the operations performed by the processor 705 can include determining an overall density of the multiphase fluid 101 at least based on a difference between the first differential pressure and the second differential pressure of the multiphase fluid 101 and the specified differential pressure height, h.
- ⁇ P is the total differential pressure loss of the multiphase fluid 101
- ⁇ is the apparent mixture density of the multiphase fluid 101
- g is acceleration due to gravity
- h v is the difference in vertical height of two reference points (such as the locations of the pressure ports 105 a , 105 b or the locations of the pressure ports 105 c , 105 d )
- ⁇ P f is the pressure loss due to miscellaneous factors, such as frictional losses and multiphase shear.
- the apparent mixture density of the multiphase fluid ( ⁇ ) can be determined by obtaining the difference between the first and second differential pressures ( ⁇ P 1 ⁇ P 2 ) and re-arranging the resulting equation to solve for ⁇ .
- the difference between the first and second differential pressures is shown by Equation 2a:
- Equation 2a Equation 2b
- Equation 2b Equation 2c:
- Equation 2d Equation 2d
- the first differential pressure ( ⁇ P 1 ) is measured by the first pair of pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the second differential pressure ( ⁇ P 2 ) is measured by the second pair of pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the acceleration of gravity is a known universal constant.
- ⁇ P 1 , ⁇ P 2 , g, and h can be input to Equation 2d to estimate the mixture density ( ⁇ ) of the multiphase fluid 101 .
- Equation 2e Equation 2e
- Equation 2e Equation 2f:
- Equation 2f Equation 2g:
- Equation 2h Re-arranging Equation 2g to solve for frictional/shear pressure losses ( ⁇ P f ) provides Equation 2h:
- ⁇ ⁇ P f ⁇ ⁇ P 1 + ⁇ ⁇ P 2 2 ( 2 ⁇ h )
- the information obtained related to frictional/shear pressure losses ( ⁇ P f ) can be useful for determining other correlations and flow characteristics of the multiphase fluid 101 .
- the information obtained related to frictional/shear pressure losses ( ⁇ P f ) can be used to determine correlations of variables used in the Venturi-type flowmeter calculations.
- Bernoulli's equation can be converted into the form shown in Equation 3a:
- m T is the total mass flow rate of the multiphase fluid 101
- C d is the discharge coefficient
- ⁇ is the expansion factor
- ⁇ P is measured pressure drop including frictional/shear pressure losses
- k f is a geometry-based correction factor to account for difference(s) in the shape/geometry of the Venturi-type flowmeter (for example, as in apparatus 100 A)
- ⁇ P f is frictional/shear pressure losses (for example, measured by apparatus 100 A and Equation 2h)
- ⁇ is the mixture density of the multiphase fluid 101 .
- the overall density ( ⁇ ) of the multiphase fluid 101 and frictional/shear pressure losses ( ⁇ P f ) determined by the apparatus 100 A can, for example, be used in conjunction with the information obtained by the Venturi-type flowmeter (for example, total mass flow rate of the multiphase fluid 101 , m T ) and be input to Equation 3a.
- the operations performed by the processor 705 can include receiving, as input, a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 .
- the operations performed by the processor 705 can include receiving, as input, a gas phase density ( ⁇ g ) of the gas phase 101 a the multiphase fluid 101 .
- the operations performed by the processor 705 can include receiving, as input, an aqueous phase density ( ⁇ a ) of the aqueous phase 101 b ′ of the multiphase fluid 101 .
- the operations performed by the processor 705 can include receiving, as input, an oil phase density ( ⁇ o ) of the oil phase 101 b ′′ of the multiphase fluid 101 .
- the operations performed by the processor 705 can include determining an aqueous phase volume fraction ( ⁇ a ) of the multiphase fluid 101 at least based on the gas phase volume fraction ( ⁇ g ), the gas density ( ⁇ g ), the aqueous phase density ( ⁇ a ), the oil phase density ( ⁇ o ), and the overall density ( ⁇ ) of the multiphase fluid 101 .
- the gas phase volume fraction ( ⁇ g ), the gas density ( ⁇ g ), the aqueous phase density ( ⁇ a ), the oil phase density ( ⁇ o ), and the overall density ( ⁇ ) of the multiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the aqueous phase volume fraction ( ⁇ a ) of the multiphase fluid 101 :
- the operations performed by the processor 705 can include receiving, as input, an aqueous phase volume fraction ( ⁇ a ) of the multiphase fluid 101 .
- the operations performed by the processor 705 can include determining a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 at least based on the aqueous phase volume fraction ( ⁇ a ), the gas density ( ⁇ g ), the aqueous phase density ( ⁇ a ), the oil phase density ( ⁇ o ), and the overall density ( ⁇ ) of the multiphase fluid 101 .
- the aqueous phase volume fraction ( ⁇ a ), the gas density ( ⁇ g ), the aqueous phase density ( ⁇ a ), the oil phase density ( ⁇ o ), and the overall density ( ⁇ ) of the multiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 .
- the first pair of pressure sensors 104 a , 104 b and the second pair of pressure sensors 104 c , 104 d measure the first differential pressure and the second differential pressure, respectively, of the multiphase fluid 101 flowing through the U-bend 102 multiple times across a time duration.
- Each of the first differential pressures and each of the second differential pressures measured by the first pair of pressure sensors 104 a , 104 b and the second pair of pressure sensors 104 c , 104 d , respectively, can be correlated to time points at which they were measured.
- Each of the first differential pressures and each of the second differential pressures measured by the first pair of pressure sensors 104 a , 104 b and the second pair of pressure sensors 104 c , 104 d , respectively, can take account for the time delay of the multiphase fluid 101 taking time to travel from the first conduit 102 a (where the first pair of pressure sensors 104 a , 104 b are located), through the connecting conduit 102 c , and to the second conduit 102 b (where the second pair of pressure sensors 104 c , 104 d are located).
- the measured differential pressures can be time-corrected to account for the delay in the multiphase fluid 101 traveling through the U-bend 102 .
- the time-series data can, for example, be stored in the memory 707 .
- the time-series data can, for example, be used to train and/or build a neural network-based classification model, which can be used to accurately identify flow regimes (for example, bubble flow, mist flow, slug flow, churn flow, annular flow, stratified flow, or intermittent flow).
- the time-series data can be converted into a spectrogram (for example, by using a Morlet wavelet transform), and a single-layer two-dimensional image can be compiled from the spectrogram.
- a neural network can then analyze the image and identify the flow regime of the multiphase fluid 101 flowing through the U-bend 102 , for example, based on comparison to historical data.
- the time-series data can, for example, be used to train and/or build a neural network-based classification model, which can be used to estimate bulk flow velocity of the multiphase fluid 101 flowing through the U-bend 102 .
- the time-series data can be converted into a spectrogram (for example, by using a Morlet wavelet transform), and a single-layer two-dimensional image can be compiled from the spectrogram.
- a neural network (machine learning model) can then analyze the image and estimate the bulk flow velocity and/or flow rate of the multiphase fluid 101 flowing through the U-bend 102 , for example, based on comparison to historical data.
- FIG. 1 B depicts an apparatus 100 B which can be used to measure a density of a multiphase fluid 101 .
- the apparatus 100 B can be substantially similar to the apparatus 100 A shown in FIG. 1 A .
- the apparatus 100 B omits the connecting conduit ( 102 c shown in FIG. 1 A ).
- the apparatus 100 B includes the U-bend 102 , which includes the first conduit 102 a and the second conduit 102 b .
- the first conduit 102 a is connected to the second conduit 102 b by a curved bend 103 .
- the first conduit 102 a , the second conduit 102 b , and the curved bend 103 are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102 .
- the curved bend 103 can be made of the same material as the first conduit 102 a and the second conduit 102 b , such that the friction experienced by the multiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same.
- the apparatus 100 B can include a first differential pressure sensor 108 a coupled to the first conduit 102 a via pressure ports 105 a and 105 b .
- the first differential pressure sensor 108 a is configured to measure a first differential pressure of the multiphase fluid 101 flowing through the U-bend 102 .
- the pressure ports 105 a and 105 b are separated by the specified differential pressure height, h, with respect to gravity.
- the apparatus 100 B can include a second differential pressure sensor 108 b coupled to the second conduit 102 b via pressure ports 105 c and 105 d .
- the second differential pressure sensor 108 b is configured to measure a second differential pressure of the multiphase fluid 101 flowing through the U-bend 102 .
- the pressure ports 105 c and 105 d are separated by the specified differential pressure height, h, with respect to gravity. As shown in FIG. 1 B , the pressure port 105 a does not necessarily need to be at the same vertical height as pressure port 105 d , and the pressure port 105 b does not necessarily need to be at the same vertical height as pressure port 105 c . Instead, the vertical distance between pressure port 105 a and pressure port 105 b should match the vertical distance between pressure port 105 c and pressure port 105 d .
- the height difference between the pressure ports 105 a , 105 b of the first differential pressure sensor 108 a and the height difference between the pressure ports 105 c , 105 d of the second differential pressure sensor 108 b are the same, such that the frictional components of the pressure drops experienced by the multiphase fluid 101 flowing through the first conduit 102 a (measured by the first differential pressure sensor 108 a ) and through the second conduit 102 b (measured by the second differential pressure sensor 108 b ) are substantially the same.
- the apparatus 100 B can be coupled to a flow pipe (such as the flow pipe 150 shown in FIG. 1 A ), for example, by angled or curved bends.
- the first and second differential pressure sensors 108 a , 108 b can be coupled to a computer (such as the computer 700 ), to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of the multiphase fluid 101 flowing through the U-bend 102 (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, or any combination of these).
- FIG. 1 C depicts an apparatus 100 C which can be used to measure a density of a multiphase fluid 101 .
- the apparatus 100 C can be substantially similar to the apparatus 100 A shown in FIG. 1 A .
- the apparatus 100 C includes multiple pairs of pressure sensors coupled to the first conduit 102 a and multiple pairs of pressure sensors coupled to the second conduit 102 b .
- the apparatus 100 C shown in FIG. 1 C includes two pairs of pressure sensors ( 104 a , 104 b and 104 a ′, 104 b ′) coupled to the first conduit 102 a installed in a parallel configuration, but can, in other embodiments, include additional pairs of pressure sensors.
- each pair of pressure sensors can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a , 104 b can be replaced by a first differential pressure sensor
- the pair of pressure sensors 104 a ′, 104 b ′ can be replaced by a second differential pressure sensor
- the pair of pressure sensors 104 c , 104 d can be replaced by a third differential pressure sensor
- the pair of pressure sensors 104 c ′, 104 d ′ can be replaced by a fourth differential pressure sensor.
- the redundancy in differential pressure sensors can be useful in providing a wider range of measurements (for example, by using sensors with different, but overlapping ranges).
- FIG. 1 D depicts an apparatus 100 D which can be used to measure a density of a multiphase fluid 101 .
- the apparatus 100 D can be substantially similar to the apparatus 100 A shown in FIG. 1 A .
- the apparatus 100 D includes more than two pressure sensors coupled to the first conduit 102 a and more than two pressure sensors coupled to the second conduit 102 b .
- the apparatus 100 D can include fewer pressure sensors (such as three, four, or five) or more pressure sensors (such as seven or more than seven) coupled to the second conduit 102 b .
- the apparatus 100 D can include fewer pressure sensors (such as three, four, or five) or more pressure sensors (such as seven or more than seven) coupled to the second conduit 102 b .
- the apparatus 100 D would include the same number of pressure sensors coupled to the first conduit 102 a as coupled to the second conduit 102 b . As shown in FIG. 1 D as including six pressure sensors ( 104 a ′, 104 b ′, 104 c ′, 104 d ′, 104 e ′, 104 f ) coupled to the second conduit 102 b .
- the apparatus 100 D can include fewer pressure sensors (such as three, four, or five) or more pressure sensors (such as seven or more than seven) coupled to the second conduit 102 b .
- the apparatus 100 D would include the same number of pressure sensors coupled to the first conduit 102 a as coupled to the second conduit 102 b . As shown in FIG.
- the pressure sensors ( 104 a , 104 b , 104 c , 104 d , 104 e , 104 f ) are installed on the first conduit 102 a in a series configuration
- the pressure sensors ( 104 a ′, 104 b ′, 104 c ′, 104 d ′, 104 e ′, 104 f ′) are installed on the second conduit 102 b in a series configuration.
- the pressure sensors 104 a and 104 b can be considered a first pair for the first conduit 102 a , corresponding to the pressure sensors 104 a ′ and 104 b ′ as a corresponding first pair for the second conduit 102 b .
- the pressure sensors 104 b and 104 c can be considered a second pair for the first conduit 102 a , corresponding to the pressure sensors 104 b ′ and 104 c ′ as a corresponding second pair for the second conduit 102 b .
- the pressure sensors 104 c and 104 d can be considered a third pair for the first conduit 102 a , corresponding to the pressure sensors 104 c ′ and 104 d ′ as a corresponding third pair for the second conduit 102 b .
- the pressure sensors 104 d and 104 e can be considered a fourth pair for the first conduit 102 a , corresponding to the pressure sensors 104 d ′ and 104 e ′ as a corresponding fourth pair for the second conduit 102 b .
- the pressure sensors 104 e and 104 f can be considered a fifth pair for the first conduit 102 a , corresponding to the pressure sensors 104 e ′ and 104 f ′ as a corresponding fifth pair for the second conduit 102 b .
- These pairs can be used to measure a piecewise pressure gradient along the first and second conduits 102 a , 102 b .
- This piecewise pressure gradient data can, for example, be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.
- the pressure sensors 104 a and 104 c can be considered a first pair for the first conduit 102 a , corresponding to the pressure sensors 104 a ′ and 104 c ′ as a corresponding first pair for the second conduit 102 b .
- the pressure sensors 104 b and 104 d can be considered a second pair for the first conduit 102 a , corresponding to the pressure sensors 104 b ′ and 104 d ′ as a corresponding second pair for the second conduit 102 b .
- the pressure sensors 104 c and 104 e can be considered a third pair for the first conduit 102 a , corresponding to the pressure sensors 104 c ′ and 104 e ′ as a corresponding third pair for the second conduit 102 b .
- the pressure sensors 104 d and 104 f can be considered a fourth pair for the first conduit 102 a , corresponding to the pressure sensors 104 d ′ and 104 f ′ as a corresponding fourth pair for the second conduit 102 b .
- these pairs can be used to measure a piecewise pressure gradient along the first and second conduits 102 a , 102 b .
- This piecewise pressure gradient data can, for example, be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.
- the pressure sensors 104 a and 104 d can be considered a first pair for the first conduit 102 a , corresponding to the pressure sensors 104 a ′ and 104 d ′ as a corresponding first pair for the second conduit 102 b .
- the pressure sensors 104 b and 104 e can be considered a second pair for the first conduit 102 a , corresponding to the pressure sensors 104 b ′ and 104 e ′ as a corresponding second pair for the second conduit 102 b .
- the pressure sensors 104 c and 104 f can be considered a third pair for the first conduit 102 a , corresponding to the pressure sensors 104 c ′ and 104 f ′ as a corresponding third pair for the second conduit 102 b .
- these pairs can be used to measure a piecewise pressure gradient along the first and second conduits 102 a , 102 b .
- This piecewise pressure gradient data can, for example, be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.
- the pressure sensors 104 a and 104 e can be considered a first pair for the first conduit 102 a , corresponding to the pressure sensors 104 a ′ and 104 e ′ as a corresponding first pair for the second conduit 102 b .
- the pressure sensors 104 b and 104 f can be considered a second pair for the first conduit 102 a , corresponding to the pressure sensors 104 b ′ and 104 f ′ as a corresponding second pair for the second conduit 102 b .
- these pairs can be used to measure a piecewise pressure gradient along the first and second conduits 102 a , 102 b .
- This piecewise pressure gradient data can, for example, be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.
- the pressure sensors 104 a and 104 f can be considered a first pair for the first conduit 102 a , corresponding to the pressure sensors 104 a ′ and 104 f ′ as a corresponding first pair for the second conduit 102 b .
- the apparatus 100 D is substantially the same as the apparatus 100 A shown in FIG. 1 A . Any combinations or sub-combinations of the aforementioned pairs or pressure sensors can be considered as suitable implementations of the apparatus 100 D.
- any pair of pressure sensors coupled to the first tubular 102 a can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a , 104 b can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a , 104 c can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a , 104 d can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a , 104 e can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a , 104 f can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b , 104 c can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b , 104 d can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b , 104 e can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b , 104 f can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 c , 104 d can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 c , 104 e can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 c , 104 f can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 d , 104 e can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 d , 104 f can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 e , 104 f can be replaced by a differential pressure sensor.
- any pair of pressure sensors coupled to the second tubular 102 b can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a ′, 104 b ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a ′, 104 c ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a ′, 104 d ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a ′, 104 e ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 a ′, 104 f ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b ′, 104 c ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b ′, 104 d ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b ′, 104 e ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 b ′, 104 f ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 c ′, 104 d ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 c ′, 104 e ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 c ′, 104 f ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 d ′, 104 e ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 d ′, 104 f ′ can be replaced by a differential pressure sensor.
- the pair of pressure sensors 104 e ′, 104 f ′ can be replaced by a differential pressure sensor.
- FIG. 1 E depicts an apparatus 100 E which can be used to measure a total mass flow rate of a multiphase fluid 101 .
- the apparatus 100 E can be substantially similar to the apparatus 100 A shown in FIG. 1 A .
- the first pair of pressure sensors 104 a , 104 b and the second pair of pressure sensors 104 c , 104 d are located at different locations on the apparatus 100 E in comparison to the apparatus 100 A.
- the first pressure sensor 104 a is coupled to the pressure port 105 a on the first pipe 150 a (third conduit) of the flow pipe 150 .
- the second pressure sensor 104 b is coupled to the pressure port 105 b on the first conduit 102 a of the U-bend 102 .
- the third pressure sensor 104 c is coupled to the pressure port 105 c on the second conduit 102 b of the U-bend 102 .
- the fourth pressure sensor 104 d is coupled to pressure port 105 d on the the second pipe 150 b (fourth conduit) of the flow pipe 150 .
- the first pair of pressure sensors 104 a , 104 b is replaced by a first differential pressure sensor.
- the second pair of pressure sensors 104 c , 104 d is replaced by a second differential pressure sensor.
- the first pair of pressure sensors 104 a , 104 b are configured to measure a first differential pressure of the multiphase fluid 101 .
- the first differential pressure includes the pressure losses of the multiphase fluid 101 flowing through the first angled bend 153 a .
- the second pair of pressure sensors 104 c , 104 d are configured to measure a second differential pressure of the multiphase fluid 101 .
- the second differential pressure includes the pressure losses of the multiphase fluid 101 flowing through the second angled bend 153 b .
- the operations performed by the processor 705 can include receiving a first differential pressure signal from the first pair of pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the first differential pressure signal can represent the first differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the operations performed by the processor 705 can include receiving a second differential pressure signal from the second pair of pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the second differential pressure signal can represent the second differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the operations performed by the processor 705 can include determining an overall flow rate of the multiphase fluid 101 at least based on the first differential pressure, the second differential pressure, a difference between the first differential pressure and the second differential pressure of the multiphase fluid 101 and the overall density of the multiphase fluid 101 .
- the overall density of the multiphase fluid 101 can be measured, for example, by a separate multiphase flowmeter.
- the apparatus 100 E can include features from the apparatus 100 A, which can be used to determine the mixture density ( ⁇ ) of the multiphase fluid 101
- the overall flow rate of the multiphase fluid 101 can be determined in various ways.
- the overall flow rate of the multiphase fluid 101 (ignoring frictional pressure loss) can be determined using the first differential pressure by Equation 4a:
- m T1 is the total mass flow rate of the multiphase fluid 101
- C d1 is an empirically characterized discharge coefficient
- ⁇ 1 is an expansion factor
- ⁇ P 1 is the first differential pressure measured by the pressure sensors 104 a , 104 b (or the first differential pressure sensor)
- ⁇ is the mixture density of the multiphase fluid 101
- g is the acceleration due to gravity
- h v is the vertical height difference between the pressure ports 105 a , 105 b to which the pressure sensors 104 a , 104 b (or the first differential pressure sensor) are coupled.
- the total mass flow rate of the multiphase fluid 101 (ignoring frictional pressure loss) can be determined using the second differential pressure by Equation 4b:
- m T2 is the total mass flow rate of the multiphase fluid 101
- C d2 is an empirically characterized discharge coefficient
- ⁇ 2 is an expansion factor
- ⁇ P 2 is the second differential pressure measured by the pressure sensors 104 c , 104 d (or the second differential pressure sensor)
- ⁇ is the mixture density of the multiphase fluid 101
- g is the acceleration due to gravity
- h v is the vertical height difference between the pressure ports 105 c , 105 d to which the pressure sensors 104 c , 104 d (or the second differential pressure sensor) are coupled.
- the operations performed by the processor 705 can include comparing the total mass flow rates (m T1 , m T2 ) determined by Equations 4a and 4b to determine an adjustment of the discharge coefficients (C d1 , C d2 ).
- the discharge coefficients (C d1 , C d2 ) can be verified for consistency and accuracy, as an in situ self-check.
- Other techniques such as least-squares minimization
- Equation 4a can be re-arranged as Equation 5a:
- Equation 4b can be re-arranged as Equation 5b:
- Equation 5c Equation 5c:
- Equation 5d Equation 5d
- Equation 5d can be used, for example, to verify the accuracy of the mixture density ( ⁇ ) determined by any one of apparatuses 100 A, 100 B, 100 C, or 100 D.
- a distance between the first pressure sensor 104 a and the second pressure sensor 104 b is substantially the same as a distance between the third pressure sensor 104 c and the fourth pressure sensor 104 d .
- the apparatus 100 E has the following dimensions.
- the inner diameter (d) of the U-bend 102 (the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c ) is about 2.067 inches (nominal pipe size (NPS) 2′′ Schedule 40).
- the inner diameter (D) of the first pipe 150 a and the second pipe 150 b is about 3.068′′ (NPS 3′′ Schedule 40).
- the dimension A is the length of straight pipe (that is, pipe that is free of any bends) of the first pipe 150 a upstream of the first pressure sensor 104 a .
- the dimension A is also the length of straight pipe of the second pipe 150 b downstream of the fourth pressure sensor 104 d .
- the dimension A is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair of pressure sensors 104 a , 104 b and the measurements taken by the second pair of pressure sensors 104 c , 104 d .
- the dimension A is at least five times the inner diameter (D) of the first pipe 150 a (A ⁇ 5D).
- the dimension B is the length of straight pipe of the first pipe 150 a downstream of the first pressure sensor 104 a and upstream of the first angled bend 153 a .
- the dimension B is also the length of straight pipe of the second pipe 150 b downstream of the second angled bend 153 b and upstream of the fourth pressure sensor 104 d .
- the dimension B is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair of pressure sensors 104 a , 104 b and the measurements taken by the second pair of pressure sensors 104 c , 104 d .
- the dimension B is at least five times the inner diameter (D) of the first pipe 150 a (B ⁇ 5D).
- the dimension C is the length of straight pipe of the first conduit 102 a downstream of the first angled bend 153 a and upstream of the second pressure sensor 104 b .
- the dimension C is also the length of straight pipe of the second conduit 102 b downstream of the third pressure sensor 104 c and upstream of the second angled bend 153 b .
- the dimension C is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair of pressure sensors 104 a , 104 b and the measurements taken by the second pair of pressure sensors 104 c , 104 d .
- the dimension C is at least five times the inner diameter (d) of the U-bend 102 (C ⁇ 5d).
- FIG. 1 F depicts an apparatus 100 F which can be used to measure a total mass flow rate of a multiphase fluid 101 .
- the apparatus 100 F can be substantially similar to the apparatus 100 E shown in FIG. 1 E . In comparison, the apparatus 100 F omits the connecting conduit ( 102 c shown in FIG. 1 E ).
- the apparatus 100 F includes the U-bend 102 , which includes the first conduit 102 a and the second conduit 102 b .
- the first conduit 102 a is connected to the second conduit 102 b by a curved bend 103 .
- the first conduit 102 a , the second conduit 102 b , and the curved bend 103 are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102 .
- the curved bend 103 can be made of the same material as the first conduit 102 a and the second conduit 102 b , such that the friction experienced by the multiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same.
- the U-bend 102 can be connected to a flow pipe 150 that flows the multiphase fluid 101 .
- the flow pipe 150 includes the first pipe 150 a and the second pipe 150 b .
- the U-bend 102 is connected to the flow pipe 150 by curved bends 153 c , 153 d .
- the first conduit 102 a of the U-bend 102 is connected to the first pipe 150 a of the flow pipe 150 by the first curved bend 153 c .
- the second conduit 102 b of the U-bend 102 is connected to the second pipe 150 b of the flow pipe 150 by the second curved bend 153 d .
- the first conduit 102 a , the second conduit 102 b , the curved bend 103 , the first curved bend 153 c , the second curved bend 153 d , and the flow pipe 150 are integrated, such that the U-bend 102 and the flow pipe 150 form a singular, unitary body, as opposed to parts that are disjointed and coupled together.
- the apparatus 100 F can include a first differential pressure sensor 108 a coupled to the first pipe 150 a and to the first conduit 102 a via pressure ports 105 a and 105 b , respectively.
- the first differential pressure sensor 108 a is configured to measure a first differential pressure of the multiphase fluid 101 flowing across the first curved bend 153 c .
- the pressure ports 105 a and 105 b are separated by the specified differential pressure height, h, with respect to gravity.
- the apparatus 100 B can include a second differential pressure sensor 108 b coupled to the second conduit 102 b and to the second pipe 150 b via pressure ports 105 c and 105 d , respectively.
- the second differential pressure sensor 108 b is configured to measure a second differential pressure of the multiphase fluid 101 flowing across the second curved bend 153 d .
- the pressure ports 105 c and 105 d are separated by the specified differential pressure height, h, with respect to gravity. As shown in FIG. 1 F , the pressure port 105 a does not necessarily need to be at the same vertical height as pressure port 105 d , and the pressure port 105 b does not necessarily need to be at the same vertical height as pressure port 105 c . Instead, the vertical distance between pressure port 105 a and pressure port 105 b should match the vertical distance between pressure port 105 c and pressure port 105 d .
- the height difference between the pressure ports 105 a , 105 b of the first differential pressure sensor 108 a and the height difference between the pressure ports 105 c , 105 d of the second differential pressure sensor 108 b are the same, and the horizontal distance between the pressure ports 105 a , 105 b of the first differential pressure sensor 108 a and the horizontal distance between the pressure ports 105 c , 105 d of the second differential pressure sensor 108 b are the same, such that the frictional components of the pressure drops experienced by the multiphase fluid 101 flowing across the first curved bend 153 c (measured by the first differential pressure sensor 108 a ) and through the second curved bend 153 d (measured by the second differential pressure sensor 108 b ) are substantially the same.
- the first and second differential pressure sensors 108 a , 108 b can be coupled to a computer (such as the computer 700 ), to determine characteristics (such as a mixture density, a total mass flow rate, or both) of the multiphase fluid 101 flowing through the U-bend 102 (for example, using Equations 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these).
- FIG. 1 G depicts an apparatus 100 G which can be used to measure a water-liquid ratio of a multiphase fluid 101 .
- the apparatus 100 G can be substantially similar to the apparatus 100 A shown in FIG. 1 A .
- the apparatus 100 G includes dynamic pressure sensors 106 a , 106 b , 106 c that are coupled to the U-bend 102 .
- the apparatus 100 G can include fewer dynamic pressure sensors (such as two dynamic pressure sensors) or more dynamic pressure sensors (such as four dynamic pressure sensors or more than four dynamic pressure sensors).
- the dynamic pressure sensors 106 a , 106 b , 106 c measure a dynamic pressure of the multiphase fluid 101 flowing through the U-bend 102 , as opposed to a static pressure of the multiphase fluid 101 .
- the dynamic pressure sensors 106 a , 106 b , 106 c can be located at any locations along the U-bend 102 .
- the dynamic pressure sensors 106 a , 106 b , 106 c are coupled to the first conduit 102 a of the U-bend 102 .
- the dynamic pressure sensors 106 a , 106 b , 106 c are coupled to the second conduit 102 b of the U-bend 102 .
- a first portion of the dynamic pressure sensors 106 a , 106 b , 106 c (for example, one or two of the dynamic pressure sensors 106 a , 106 b , 106 c ) is coupled to the first conduit 102 a of the U-bend 102 , and a remaining portion of the dynamic pressure sensors 106 a , 106 b , 106 c is coupled to the second conduit 102 b of the U-bend 102 .
- the dynamic pressure sensors 106 a , 106 b , 106 c can be evenly or randomly distributed along the U-bend 102.
- the dynamic pressure measurements taken by the dynamic pressure sensors 106 a , 106 b , 106 c can be cross-correlated (for example, by the processor 705 ) to determine a speed of sound of the multiphase fluid 101 flowing through the U-bend 102 .
- the speed of sound of the multiphase fluid 101 and the overall density ( ⁇ ) of the multiphase fluid 101 can then be used to determine the water-liquid ratio of the multiphase fluid 101 .
- the water-liquid ratio of the multiphase fluid 101 is a ratio of a volume of the aqueous phase 101 b ′ to a sum of the volume of the aqueous phase 101 b ′ and a volume of the oil phase 101 b ′′ (liquid phase 101 b ) (that is, the ratio of (volume of 101 b ′)/(volume of 101 b ′+volume of 101 b ′′), which is the same as the ratio of (volume of 101 b ′)/(volume of 101 b )).
- the speed of sound of the multiphase fluid 101 and the overall density ( ⁇ ) of the multiphase fluid 101 can be compared to a plotted graph of various phase curves (gas/oil, gas/aqueous, oil/aqueous) to determine the water-liquid ratio.
- FIG. 1 H depicts an apparatus 100 H which can be used to measure a density, a total flow rate, and phase flow rates of a multiphase fluid 101 .
- the apparatus 100 H can be substantially similar to the apparatus 100 A shown in FIG. 1 A and the apparatus 100 E shown in FIG. 1 E .
- the apparatus 100 H can be a combination of the apparatus 100 A and the apparatus 100 E.
- the first pressure sensor 104 a is coupled to a first pressure port 105 a on the first pipe 150 a (third conduit) of the flow pipe 150 .
- the second pressure sensor 104 b is coupled to a second pressure port 105 b on the first conduit 102 a of the U-bend 102 .
- the third pressure sensor 104 c is coupled to a third pressure port 105 c on the second conduit 102 b of the U-bend 102 .
- the fourth pressure sensor 104 d is coupled to a fourth pressure port 105 d on the second pipe 150 b (fourth conduit) of the flow pipe 150 .
- the fifth and sixth pressure sensors 104 e , 104 f are coupled to fifth and sixth pressure ports 105 e , 105 f , respectively, on the first conduit 102 a of the U-bend 102 .
- the fifth and sixth pressure ports 105 e , 105 f are separated by the specified height, h, along the first conduit 102 a .
- the seventh and eighth pressure sensors 104 g , 104 h are coupled to seventh and eighth pressure ports 105 g , 105 h , respectively, on the second conduit 102 b of the U-bend 102 .
- the seventh and eighth pressure ports 105 g , 105 h are separated by the specified height, h, along the second conduit 102 b .
- the first and second pressure sensors 104 a , 104 b are replaced by a first differential pressure sensor.
- the third and fourth pressure sensors 104 c , 104 d are replaced by a second differential pressure sensor.
- the fifth and sixth pressure sensors 104 e , 104 f are replaced by a third differential pressure sensor.
- the seventh and eighth pressure sensors 104 g , 104 h are replaced by a fourth differential pressure sensor.
- the first pair of pressure sensors 104 a , 104 b are configured to measure a first differential pressure of the multiphase fluid 101 .
- the first differential pressure includes the pressure losses of the multiphase fluid 101 flowing through the first angled bend 153 a .
- the second pair of pressure sensors 104 c , 104 d are configured to measure a second differential pressure of the multiphase fluid 101 .
- the second differential pressure includes the pressure losses of the multiphase fluid 101 flowing through the second angled bend 153 b .
- the third pair of pressure sensors 104 e , 104 f are configured to measure a third differential pressure of the multiphase fluid 101 .
- the fourth pair of pressure sensors 104 g , 104 h are configured to measure a fourth differential pressure of the multiphase fluid 101 .
- the operations performed by the processor 705 can include receiving a first differential pressure signal from the first pair of pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the first differential pressure signal can represent the first differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 a , 104 b (or first differential pressure sensor).
- the operations performed by the processor 705 can include receiving a second differential pressure signal from the second pair of pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the second differential pressure signal can represent the second differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 c , 104 d (or second differential pressure sensor).
- the operations performed by the processor 705 can include receiving a third differential pressure signal from the third pair of pressure sensors 104 e , 104 f (or third differential pressure sensor).
- the third differential pressure signal can represent the third differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 e , 104 f (or third differential pressure sensor).
- the operations performed by the processor 705 can include receiving a fourth differential pressure signal from the fourth pair of pressure sensors 104 g , 104 h (or fourth differential pressure sensor).
- the fourth differential pressure signal can represent the fourth differential pressure of the multiphase fluid 101 measured by the pressure sensors 104 g , 104 h (or fourth differential pressure sensor).
- the operations performed by the processor 705 can include determining an overall density of the multiphase fluid 101 at least based on the specified height (h) and a difference between the third differential pressure and the fourth differential pressure.
- the operations performed by the processor 705 can include determining an overall flow rate of the multiphase fluid 101 at least based on the first differential pressure and the second differential pressure of the multiphase fluid 101 and the overall density of the multiphase fluid 101 .
- the mixture density of the multiphase fluid 101 can be determined in various ways.
- the mixture density ( ⁇ ) of the multiphase fluid 101 can be determined by Equation 2d tailored for the apparatus 100 H, where ⁇ P 1 is the third differential pressure measured by the third pair of pressure sensors 104 e , 104 f (or third differential pressure sensor), ⁇ P 2 is the fourth differential pressure measured by the fourth pair of pressure sensors 104 g , 104 h (or fourth differential pressure sensor), and h 2 is the specified height (h).
- the mixture density ( ⁇ ) of the multiphase fluid 101 can be determined by Equation 5d tailored for the apparatus 100 H, where ⁇ P 1 is the third differential pressure measured by the third pair of pressure sensors 104 e , 104 f (or third differential pressure sensor) and ⁇ P 2 is the fourth differential pressure measured by the fourth pair of pressure sensors 104 g , 104 h (or fourth differential pressure sensor).
- the total flow rate of the multiphase fluid 101 can be determined in various ways. As a first example, the total flow rate of the multiphase fluid 101 can be determined using the first differential pressure by Equation 4a. As a second example, the total flow rate of the multiphase fluid 101 can be determined using the second differential pressure by Equation 4b.
- the operations performed by the processor 705 can include comparing the overall flow rates (m T1 , m T2 ) determined by Equations 4a and 4bc to determine an adjustment of the discharge coefficients (C d1 , C d2 ).
- a distance between the first pressure sensor 104 a and the second pressure sensor 104 b is substantially the same as a distance between the third pressure sensor 104 c and the fourth pressure sensor 104 d .
- the apparatus 100 D has the following dimensions.
- the inner diameter (d) of the U-bend 102 (the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c ) is about 2.067 inches (NPS 2′′ Schedule 40).
- the inner diameter (D) of the first pipe 150 a and the second pipe 150 b is about 3.068′′ (NPS 3′′ Schedule 40).
- the dimension A is the length of straight pipe (that is, pipe that is free of any bends) of the first pipe 150 a upstream of the first pressure sensor 104 a .
- the dimension A is also the length of straight pipe of the second pipe 150 b downstream of the fourth pressure sensor 104 d .
- the dimension A is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair of pressure sensors 104 a , 104 b and the measurements taken by the second pair of pressure sensors 104 c , 104 d .
- the dimension A is at least five times the inner diameter (D) of the first pipe 150 a (A ⁇ 5D).
- the dimension B is the length of straight pipe of the first pipe 150 a downstream of the first pressure sensor 104 a and upstream of the first angled bend 153 a .
- the dimension B is also the length of straight pipe of the second pipe 150 b downstream of the second angled bend 153 b and upstream of the fourth pressure sensor 104 d .
- the dimension B is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair of pressure sensors 104 a , 104 b and the measurements taken by the second pair of pressure sensors 104 c , 104 d .
- the dimension B is at least five times the inner diameter (D) of the first pipe 150 a (B ⁇ 5D).
- the dimension C is the length of straight pipe of the first conduit 102 a downstream of the first angled bend 153 a and upstream of the second pressure sensor 104 b .
- the dimension C is also the length of straight pipe of the second conduit 102 b downstream of the third pressure sensor 104 c and upstream of the second angled bend 153 b .
- the dimension C is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair of pressure sensors 104 a , 104 b and the measurements taken by the second pair of pressure sensors 104 c , 104 d .
- the dimension C is at least five times the inner diameter (d) of the U-bend 102 (C ⁇ 5d).
- the dimension E is the length of straight pipe of the first conduit 102 a downstream of the sixth pressure sensor 104 f and upstream of the first curved bend 103 a .
- the dimension E is also the length of straight pipe of the second conduit 102 b downstream of the second curved bend 103 b and upstream of the seventh pressure sensor 104 g .
- the dimension E is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the third pair of pressure sensors 104 e , 104 f and the measurements taken by the fourth pair of pressure sensors 104 g , 104 h .
- the dimension E is at least five times the inner diameter (d) of the U-bend 102 (E ⁇ 5d).
- FIG. 1 I depicts an apparatus 100 I which can be used to measure a density, a flow rate, and a water-liquid ratio of a multiphase fluid 101 .
- the apparatus 100 I can be substantially similar to the apparatus 100 A shown in FIG. 1 A , the apparatus 100 E shown in FIG. 1 E , the apparatus 100 G shown in FIG. 1 G , and the apparatus 100 H shown in FIG. 1 H .
- the apparatus 100 I can be a combination of the apparatus 100 G and the apparatus 100 H.
- the apparatus 100 I can be a copy of the apparatus 100 H that also includes dynamic pressure sensors 106 a , 106 b , 106 c (similar to the apparatus 100 G) that are coupled to the U-bend 102 .
- the apparatus 100 I can perform all of the functions that can be performed by the apparatus 100 G and also by the apparatus 100 H.
- the apparatus 100 I can include fewer dynamic pressure sensors (such as two dynamic pressure sensors) or more dynamic pressure sensors (such as four dynamic pressure sensors or more than four dynamic pressure sensors).
- the dynamic pressure sensors 106 a , 106 b , 106 c measure a dynamic pressure of the multiphase fluid 101 flowing through the U-bend 102 , as opposed to a static pressure of the multiphase fluid 101 .
- the dynamic pressure sensors 106 a , 106 b , 106 c can be located at any locations along the U-bend 102 .
- the dynamic pressure sensors 106 a , 106 b , 106 c are coupled to the first conduit 102 a of the U-bend 102 . In some implementations, the dynamic pressure sensors 106 a , 106 b , 106 c are coupled to the second conduit 102 b of the U-bend 102 .
- a first portion of the dynamic pressure sensors 106 a , 106 b , 106 c (for example, one or two of the dynamic pressure sensors 106 a , 106 b , 106 c ) is coupled to the first conduit 102 a of the U-bend 102 , and a remaining portion of the dynamic pressure sensors 106 a , 106 b , 106 c is coupled to the second conduit 102 b of the U-bend 102 .
- the dynamic pressure sensors 106 a , 106 b , 106 c can be evenly or randomly distributed along the U-bend 102 .
- the dynamic pressure measurements taken by the dynamic pressure sensors 106 a , 106 b , 106 c can be cross-correlated (for example, by the processor 705 ) to determine a speed of sound of the multiphase fluid 101 flowing through the U-bend 102 .
- the speed of sound of the multiphase fluid 101 and the overall density ( ⁇ ) of the multiphase fluid 101 can then be used to determine the water-liquid ratio of the multiphase fluid 101 .
- the speed of sound of the multiphase fluid 101 and the overall density ( ⁇ ) of the multiphase fluid 101 can be compared to a plotted graph of various phase curves (gas/oil, gas/aqueous, oil/aqueous) to determine the water-liquid ratio.
- FIG. 1 J depicts an apparatus 100 J which can be used to measure a density, a flow rate, and a water-liquid ratio of a multiphase fluid 101 .
- the apparatus 100 J can be substantially similar to the apparatus 100 H shown in FIG. 1 H .
- the apparatus 100 J omits the connecting conduit ( 102 c shown in FIG. 1 H ).
- the apparatus 100 J includes the U-bend 102 , which includes the first conduit 102 a and the second conduit 102 b .
- the first conduit 102 a is connected to the second conduit 102 b by a curved bend 103 .
- the first conduit 102 a , the second conduit 102 b , and the curved bend 103 are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102 .
- the curved bend 103 can be made of the same material as the first conduit 102 a and the second conduit 102 b , such that the friction experienced by the multiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same.
- the U-bend 102 can be connected to a flow pipe 150 that flows the multiphase fluid 101 .
- the flow pipe 150 includes the first pipe 150 a and the second pipe 150 b .
- the U-bend 102 is connected to the flow pipe 150 by curved bends 153 c , 153 d .
- the first conduit 102 a of the U-bend 102 is connected to the first pipe 150 a of the flow pipe 150 by the first curved bend 153 c .
- the second conduit 102 b of the U-bend 102 is connected to the second pipe 150 b of the flow pipe 150 by the second curved bend 153 d .
- the first conduit 102 a , the second conduit 102 b , the curved bend 103 , the first curved bend 153 c , the second curved bend 153 d , and the flow pipe 150 are integrated, such that the U-bend 102 and the flow pipe 150 form a singular, unitary body, as opposed to parts that are disjointed and coupled together.
- the apparatus 100 J can include a first differential pressure sensor 108 a coupled to the first pipe 150 a and to the first conduit 102 a via pressure ports 105 a and 105 b , respectively.
- the first differential pressure sensor 108 a is configured to measure a first differential pressure of the multiphase fluid 101 flowing across the first curved bend 153 c .
- the pressure ports 105 a and 105 b are separated by the specified differential pressure height, h, with respect to gravity.
- the apparatus 100 B can include a second differential pressure sensor 108 b coupled to the second conduit 102 b and to the second pipe 150 b via pressure ports 105 c and 105 d , respectively.
- the second differential pressure sensor 108 b is configured to measure a second differential pressure of the multiphase fluid 101 flowing across the second curved bend 153 d .
- the pressure ports 105 c and 105 d are separated by the specified differential pressure height, h, with respect to gravity. As shown in FIG. 1 F , the pressure port 105 a does not necessarily need to be at the same vertical height as pressure port 105 d , and the pressure port 105 b does not necessarily need to be at the same vertical height as pressure port 105 c . Instead, the vertical distance between pressure port 105 a and pressure port 105 b should match the vertical distance between pressure port 105 c and pressure port 105 d .
- the height difference between the pressure ports 105 a , 105 b of the first differential pressure sensor 108 a and the height difference between the pressure ports 105 c , 105 d of the second differential pressure sensor 108 b are the same, and the horizontal distance between the pressure ports 105 a , 105 b of the first differential pressure sensor 108 a and the horizontal distance between the pressure ports 105 c , 105 d of the second differential pressure sensor 108 b are the same, such that the frictional components of the pressure drops experienced by the multiphase fluid 101 flowing across the first curved bend 153 c (measured by the first differential pressure sensor 108 a ) and through the second curved bend 153 d (measured by the second differential pressure sensor 108 b ) are substantially the same.
- the apparatus 100 J can include a third differential pressure sensor 108 c coupled to the first conduit 102 a via pressure ports 105 e and 105 f .
- the third differential pressure sensor 108 c is configured to measure a third differential pressure of the multiphase fluid 101 flowing through the U-bend 102 .
- the pressure ports 105 e and 105 f are separated by the specified differential pressure height, h, with respect to gravity.
- the apparatus 100 J can include a fourth differential pressure sensor 108 d coupled to the second conduit 102 b via pressure ports 105 g and 105 h .
- the fourth differential pressure sensor 108 d is configured to measure a fourth differential pressure of the multiphase fluid 101 flowing through the U-bend 102 .
- the pressure ports 105 g and 105 h are separated by the specified differential pressure height, h, with respect to gravity. As shown in FIG. 1 J , the pressure port 105 e does not necessarily need to be at the same vertical height as pressure port 105 h , and the pressure port 105 f does not necessarily need to be at the same vertical height as pressure port 105 g . Instead, the vertical distance between pressure port 105 e and pressure port 105 f should match the vertical distance between pressure port 105 g and pressure port 105 h .
- the height difference between the pressure ports 105 e , 105 f of the third differential pressure sensor 108 c and the height difference between the pressure ports 105 g , 105 h of the fourth differential pressure sensor 108 d are the same, such that the frictional components of the pressure drops experienced by the multiphase fluid 101 flowing through the first conduit 102 a (measured by the third differential pressure sensor 108 c ) and through the second conduit 102 b (measured by the fourth differential pressure sensor 108 d ) are substantially the same.
- the first, second, third, and fourth differential pressure sensors 108 a , 108 b , 108 c , 108 d can be coupled to a computer (such as the computer 700 ), to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of the multiphase fluid 101 flowing through the U-bend 102 (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these).
- any of the apparatuses 100 A, 100 B, 100 C, 100 D, 100 E, 100 F, 100 G, 100 H, 100 I, or 100 J can be combined with any of the following components to obtain additional information about the multiphase fluid 101 : a flowmeter (such as a Venturi-type meter), a water-cut meter that measures water fraction or water-liquid ratio, a dynamic pressure sensor, a temperature sensor, or a strain gauge.
- a flowmeter such as a Venturi-type meter
- a water-cut meter that measures water fraction or water-liquid ratio
- a dynamic pressure sensor a temperature sensor
- the dynamic pressure sensor can be located on the same pressure tap as any of the pressure sensors already included in the apparatus ( 100 A, 100 B, 100 C, 100 D, 100 E, 100 F, 100 G, 100 H, 100 I, or 100 J).
- FIG. 2 A is a schematic diagram depicting various example pressure tap arrangements.
- Each of the views (i), (ii), and (iii) are cross-sectional views of a pipe (for example, the first conduit 102 a or the second conduit 102 b ).
- Any of the pressure sensors ( 104 a , 104 b , 104 c , 104 d , 104 e , 104 f , 104 a ′, 104 b ′, 104 c ′, 104 d ′, 104 e ′, 104 f ′) can have the form shown in view (i), (ii), or (iii).
- the pressure sensor includes a single pressure tap.
- the pressure sensor includes various pressure taps (for example, four) that are distributed around a circumference of the conduit.
- the pressure sensor can obtain four simultaneous readings (one at each of the four pressure taps) and average the four simultaneous readings to obtain an averaged pressure reading for that particular axial location along the conduit.
- the pressure sensors can have fewer pressure taps (such as two or three) or more pressure taps (such as five or more than five).
- the pressure sensor includes a circumferential pressure tap that fully spans the entire circumference of the conduit. The circumferential pressure tap shown in view (iii) may be the most accurate out of all the views (i), (ii), and (iii) shown in FIG. 2 A .
- FIG. 2 B is a schematic diagram depicting various example piping arrangements.
- Each of the views (i), (ii), (iii), (iv), and (v) depict piping arrangements that can used in addition to or alternatively to the piping arrangements already described with respect to the apparatuses 100 A, 100 B, 100 C, 100 D, 100 E, 100 F, 100 G, 100 H, 100 I, and 100 J.
- ⁇ P 1 is a first differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement.
- ⁇ P 2 is a second differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement.
- ⁇ P 1 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 2 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of the multiphase fluid 101 flowing through the respective piping arrangement (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, or any combination of these).
- view (i) can be considered a base case that generally conforms to the piping arrangements of apparatuses 100 A and 100 B shown in FIGS. 1 A and 1 B , respectively.
- the piping arrangement of view (ii) is substantially similar to the piping arrangement of view (i), but the first and second conduits 102 a , 102 b of view (ii) are not necessarily straight pipes.
- the connecting conduit ( 102 c ) is omitted, and the first and second conduits 102 a , 102 b are connected by an angled bend.
- the piping arrangement of view (iv) is substantially similar to the piping arrangement of view (i), but is flipped vertically, such that the multiphase fluid 101 flowing through the piping arrangement of view (iv) flows downward before flowing upward.
- the piping arrangement of view (v) is substantially similar to the piping arrangement of view (i), but the first and second conduits 102 a , 102 b are coiled (that is, includes coiled piping).
- FIG. 2 C is a schematic diagram depicting various example piping arrangements.
- Each of the views (i), (ii), (iii), (iv), and (v) depict piping arrangements that can used in addition to or alternatively to the piping arrangements already described with respect to the apparatuses 100 A, 100 B, 100 C, 100 D, 100 E, 100 F, 100 G, 100 H, 100 I, and 100 J.
- ⁇ P 1 is a first differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement across a first bend (curved or angled).
- ⁇ P 2 is a second differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement across a second bend (curved or angled).
- ⁇ P 1 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 2 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, or both) of the multiphase fluid 101 flowing through the respective piping arrangement (for example, using Equations 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these).
- view (i) can be considered a base case that generally conforms to the piping arrangements of apparatuses 100 E and 100 F shown in FIGS. 1 E and 1 F , respectively.
- the piping arrangement of view (ii) is substantially similar to the piping arrangement of view (i), but the first and second conduits 102 a , 102 b of view (ii) deviate from vertically oriented pipes (that is, they are disposed at non-zero angles with respect to a vertical) and are not necessarily straight pipes.
- the first and second conduits 102 a , 102 b deviate from vertically oriented pipes, but are straight pipes that are connected with angled bends.
- the piping arrangement of view (iv) is substantially similar to the piping arrangement of view (i), but is flipped vertically, such that the multiphase fluid 101 flowing through the piping arrangement of view (iv) flows downward before flowing upward.
- the piping arrangement of view (v) is substantially similar to the piping arrangement of view (i), but the first and second conduits 102 a , 102 b are coiled (that is, includes coiled piping).
- FIG. 2 D is a schematic diagram depicting various example piping arrangements.
- ⁇ P 1 is a first differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement across a first bend (curved or angled).
- ⁇ P 2 is a second differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement across a second bend (curved or angled).
- ⁇ P 1 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 2 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 3 is a third differential pressure of the multiphase fluid 101 flowing through the first conduit 102 a of the respective piping arrangement.
- ⁇ P 4 is a fourth differential pressure of the multiphase fluid 101 flowing through the second conduit 102 b of the respective piping arrangement.
- ⁇ P 3 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 4 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- the first, second, third, and fourth differential pressures ( ⁇ P 1 , ⁇ P 2 , ⁇ P 3 , ⁇ P 4 ) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of the multiphase fluid 101 flowing through the respective piping arrangement (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these).
- view (i) can be considered a base case that generally conforms to the piping arrangements of apparatuses 100 H and 100 J shown in FIGS. 1 H and 1 J , respectively.
- the piping arrangement of view (ii) is substantially similar to the piping arrangement of view (i), but the first and second conduits 102 a , 102 b of view (ii) deviate from vertically oriented pipes and are connected with angled bends.
- the first and second pipes 150 a , 150 b of the flow pipe 150 are not in-line with one another.
- the piping arrangement of view (iv) is substantially similar to the piping arrangement of view (i), but is flipped vertically, such that the multiphase fluid 101 flowing through the piping arrangement of view (iv) flows downward before flowing upward.
- FIG. 2 E is a schematic diagram depicting various example piping arrangements.
- ⁇ P 1 is a first differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement across a first bend (curved or angled).
- ⁇ P 2 is a second differential pressure of the multiphase fluid 101 flowing through the respective piping arrangement across a second bend (curved or angled).
- ⁇ P 1 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 2 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 3 is a third differential pressure of the multiphase fluid 101 flowing through the first conduit 102 a of the respective piping arrangement.
- ⁇ P 4 is a fourth differential pressure of the multiphase fluid 101 flowing through the second conduit 102 b of the respective piping arrangement.
- ⁇ P 3 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- ⁇ P 4 can be measured by a pair of pressure sensors or a single differential pressure sensor.
- the first, second, third, and fourth differential pressures ( ⁇ P 1 , ⁇ P 2 , ⁇ P 3 , ⁇ P 4 ) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of the multiphase fluid 101 flowing through the respective piping arrangement (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these).
- the piping arrangement of view (i) is substantially similar to the piping arrangements of apparatuses 100 H and 100 J shown in FIGS. 1 H and 1 J , respectively, but the first and second conduits 102 a , 102 b of view (i) are not necessarily straight pipes.
- the first and second conduits 102 a , 102 b form a loop.
- the piping arrangement of view (iii) is substantially similar to the piping arrangement of view (i) of FIG. 2 D , but the first and second conduits 102 a , 102 b are coiled (that is, includes coiled piping).
- the piping arrangement of view (iv) is substantially similar to the piping arrangement of view (ii), but the first and second conduits 102 a , 102 b form an angled loop with straight portions of piping in between angled bends. Further, in the piping arrangement of view (iv), the first and second pipes 150 a , 150 b of the flow pipe 150 are not in-line with one another
- FIG. 2 F is a schematic diagram depicting various example sensor arrangements. Any of the sensor arrangements shown in views (i), (ii), (iii), (iv), and (v) can be applied (either alone or in combination) in addition to or alternatively to the sensor arrangements already described with respect to the apparatuses 100 A, 100 B, 100 C, 100 D, 100 E, 100 F, 100 G, 100 H, 100 I, and 100 J.
- view (i) can be considered a base case that generally conforms to the differential pressure sensor arrangements of apparatuses 100 B, 100 F, and 100 J shown in FIGS. 1 B, 1 F, and 1 J , respectively.
- the pressure sensor arrangement of view (ii) includes two pressure sensors which measure static pressure at their respective locations. A difference between the measured static pressures can be determined as a differential pressure (similar to the differential pressure sensor).
- the pressure sensor arrangement of view (ii) is substantially similar to the pressure sensor arrangements shown in the apparatuses 100 A, 100 C, 100 D, 100 E, 100 G, 100 H, and 100 I shown in FIGS. 1 A, 1 C, 1 D, 1 E, 1 G, 1 H, and 1 I , respectively.
- the differential pressure sensor arrangement of view (iii) is substantially similar to the view (i) but includes redundant differential pressure sensors in a parallel configuration across the same length of piping, which is substantially similar to the differential pressure sensor arrangement shown in apparatus 100 C of FIG. 1 C .
- the differential pressure sensor arrangement of view (iv) is substantially similar to the differential pressure sensor arrangement of view (i), but includes additional differential pressure sensors in a series configuration across a length of piping, which is substantially similar to the differential pressure sensor arrangement shown in apparatus 100 D of FIG. 1 D .
- the sensor arrangement of view (v) includes multiple strain sensors (such as strain gauges) disposed along a length of piping. The measured strain can be correlated to pressure, such that similar calculations can be completed to determine characteristics of the flowing multiphase fluid 101 .
- FIG. 3 A is a flowchart depicting an example multiphase fluid flow model 300 A.
- Any one of the apparatuses 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 A to characterize a multiphase fluid, such as the multiphase fluid 101 .
- pressure and temperature of the multiphase fluid 101 is determined (for example, using pressure and temperature sensors).
- various properties (such as the density, viscosity, and speed of sound) of the phases (gas phase 101 a , aqueous phase 101 b ′, and oil phase 101 b ′′) of the multiphase fluid 101 are determined.
- the gas phase density ( ⁇ g ) of the gas phase 101 a , the aqueous phase density ( ⁇ a ) of the aqueous phase 101 b ′, and the oil phase density ( ⁇ o ) of the oil phase 101 b ′′ are determined at block 303 a .
- a total flow rate (m T ) of the multiphase fluid 101 is determined (for example, using differential pressure sensors as in the apparatus 100 D).
- a mixture density ( ⁇ ) of the multiphase fluid 101 is determined (for example, using differential pressure sensors as in the apparatus 100 A).
- a water-liquid ratio (R WL ) of the multiphase fluid 101 is determined (for example, using dynamic pressure sensors as in the apparatus 100 E)).
- FIG. 3 B is a flowchart depicting an example multiphase fluid flow model 300 B.
- Any one of the apparatuses 100 A, 100 B, 100 C, 100 D, 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 B to characterize a multiphase fluid, such as the multiphase fluid 101 .
- a first differential pressure ( ⁇ P 1 ) and a second differential pressure ( ⁇ P 2 ) of the flowing multiphase fluid 101 is measured.
- the first differential pressure ( ⁇ P 1 ) is measured in a first direction across a specified differential pressure height (h).
- the second differential pressure ( ⁇ P 2 ) is measured in a second direction (different from the first direction) across the specified differential pressure height (h).
- the first and second directions are such that the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction.
- the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction.
- the multiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction.
- a frictional pressure loss ( ⁇ P f ) of the flowing multiphase fluid 101 is calculated based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 b .
- the frictional pressure loss ( ⁇ P f ) can be calculated at block 303 b , for example, by Equation 2h.
- a mixture density ( ⁇ ) of the multiphase fluid 101 is calculated based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 b .
- the mixture density ( ⁇ ) can be calculated at block 305 b , for example, by Equation 2d.
- a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the mixture density ( ⁇ ) determined at block 305 b .
- the gas phase volume fraction ( ⁇ g ) can be calculated at block 307 b , for example, by Equation 3b.
- gas phase volume fraction ( ⁇ g ) can be calculated at block 307 b based on other known or measured parameters, such as density of the liquid phase ( ⁇ l ) and density of the gas phase ( ⁇ g ).
- the gas phase volume fraction ( ⁇ g ) can be calculated by Equation 6a.
- ⁇ g ⁇ - ⁇ l ⁇ g - ⁇ l ( 6 ⁇ a )
- a total mass flow rate (m T ) of the multiphase fluid 101 is determined.
- the total mass flow rate (m T ) can be determined, for example, by a mass flowmeter and/or by any of Equations 3a, 4a, or 4b.
- the multiphase fluid flow model 300 B assumes that a slip ratio (S) of the multiphase fluid 101 is substantially equal to 1.
- the slip ratio (S) is the ratio of the velocity of the gas phase to the velocity of the liquid phase (including the aqueous phase and the oil phase) in the flowing multiphase fluid 101 .
- FIG. 3 C is a flowchart depicting an example multiphase fluid flow model 300 C.
- Any one of the apparatuses 100 A, 100 B, 100 C, 100 D, 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 C to characterize a multiphase fluid, such as the multiphase fluid 101 .
- a first differential pressure ( ⁇ P 1 ) and a second differential pressure ( ⁇ P 2 ) of the flowing multiphase fluid 101 is measured.
- the first differential pressure ( ⁇ P 1 ) is measured in a first direction across a specified differential pressure height (h).
- the second differential pressure ( ⁇ P 2 ) is measured in a second direction (different from the first direction) across the specified differential pressure height (h).
- the first and second directions are such that the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction.
- the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction.
- the multiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction.
- a frictional pressure loss ( ⁇ P f ) of the flowing multiphase fluid 101 is calculated based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 c .
- the frictional pressure loss ( ⁇ P f ) can be calculated at block 303 c , for example, by Equation 2h.
- an apparent mixture density ( ⁇ app ) of the multiphase fluid 101 is estimated based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 c .
- the apparent mixture density ( ⁇ app ) can be estimated at block 305 c , for example, by Equation 2d.
- a void fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the apparent mixture density ( ⁇ app ) estimated at block 305 c .
- the void fraction ( ⁇ g ) can be calculated at block 307 c , for example, by Equation 6b.
- ⁇ g ⁇ app - ⁇ l ⁇ g - ⁇ l ( 6 ⁇ b )
- various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowing multiphase fluid 101 are determined.
- the conditions and/or properties determined at block 309 c can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers).
- a water-liquid ratio (R WL ) of the flowing multiphase fluid 101 is determined.
- the water-liquid ratio (R WL ) can be determined at block 311 c can be measured, for example, by external sensors (such as dynamic pressure sensors, as in apparatus 100 G shown in FIG. 1 G ).
- densities of the various phases (such as density of the gas phase ( ⁇ g ), density of the aqueous phase ( ⁇ a ), and density of the oil phase ( ⁇ o )) of the flowing multiphase fluid 101 are determined.
- the densities of the various phases of the flowing multiphase fluid 101 can be determined at block 313 c , for example, based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 309 c .
- a density of the liquid phase ( ⁇ l , including the aqueous phase and the oil phase) is determined.
- the density of the liquid phase ( ⁇ l ) can be determined at block 313 c based on the densities of the various phases of the flowing multiphase fluid 101 and the water-liquid ratio (R WL ) determined at block 311 c .
- the density of the liquid phase ( ⁇ l ) can be determined at block 313 c by Equation 6c.
- the void fraction ( ⁇ g ) can be calculated at block 307 c based on the density of the liquid phase ( ⁇ l ) and the density of the gas phase ( ⁇ g ) determined at block 313 c.
- a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the void fraction ( ⁇ g ) determined at block 307 c and slip ratio (S) of the flowing multiphase fluid 101 .
- the slip ratio (S) used at block 315 c to determine the gas phase volume fraction ( ⁇ g ) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess.
- a mixture density ( ⁇ ) of the multiphase fluid 101 is calculated based on the gas phase volume fraction ( ⁇ g ) determined at block 315 c , the density of the gas phase ( ⁇ g ) determined at block 313 c , and the density of the liquid phase ( ⁇ l ) determined at block 313 c .
- the mixture density ( ⁇ ) can be determined at block 317 c by Equation 6d.
- a total mass flow rate (m T ) of the multiphase fluid 101 is determined.
- the total mass flow rate (m T ) can be determined, for example, by a mass flowmeter and/or by any of Equations 3a, 4a, or 4b.
- the blocks in the dotted box of the multiphase fluid flow model 300 C (blocks 315 c , 317 c , determining the total mass flow rate (m T ), and determining the slip ratio (S)) are performed simultaneously (for example, in parallel).
- the blocks in the dotted box of the multiphase fluid flow model 300 C (blocks 315 c , 317 c , determining the total mass flow rate (m T ), and determining the slip ratio (5)) are performed iteratively (for example, in series) until the calculated values converge to final values.
- FIG. 3 D is a flowchart depicting an example multiphase fluid flow model 300 D.
- Any one of the apparatuses 100 A, 100 B, 100 C, 100 D, 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 D to characterize a multiphase fluid, such as the multiphase fluid 101 .
- a first differential pressure ( ⁇ P 1 ) and a second differential pressure ( ⁇ P 2 ) of the flowing multiphase fluid 101 is measured.
- the first differential pressure ( ⁇ P 1 ) is measured in a first direction across a specified differential pressure height (h).
- the second differential pressure ( ⁇ P 2 ) is measured in a second direction (different from the first direction) across the specified differential pressure height (h).
- the first and second directions are such that the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction.
- the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction.
- the multiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction.
- a frictional pressure loss ( ⁇ P f ) of the flowing multiphase fluid 101 is calculated based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 d .
- the frictional pressure loss ( ⁇ P f ) can be calculated at block 303 d , for example, by Equation 2h.
- an apparent mixture density ( ⁇ app ) of the multiphase fluid 101 is estimated based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 d .
- the apparent mixture density ( ⁇ app ) can be estimated at block 305 d , for example, by Equation 2d.
- various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowing multiphase fluid 101 are determined.
- the conditions and/or properties determined at block 307 d can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers).
- densities of the various phases (such as density of the gas phase ( ⁇ g ), density of the aqueous phase ( ⁇ a ), and density of the oil phase ( ⁇ o )) of the flowing multiphase fluid 101 are determined.
- the densities of the various phases of the flowing multiphase fluid 101 can be determined at block 309 d , for example, based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 307 d .
- a gas phase volume fraction ( ⁇ g ) of the flowing multiphase fluid 101 is determined.
- the gas phase volume fraction ( ⁇ g ) determined at block 311 d can be measured, for example, by an external sensor (such as an ultrasonic sensor).
- a void fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the gas volume fraction fraction ( ⁇ g ) determined at block 311 d and slip ratio (S) of the flowing multiphase fluid 101 .
- the slip ratio (S) used at block 313 d to determine the void fraction ( ⁇ g ) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess.
- a density of the liquid phase ( ⁇ l , including the aqueous phase and the oil phase) is determined.
- the density of the liquid phase ( ⁇ l ) can be determined at block 315 d based on the apparent mixture density ( ⁇ app ) determined at block 305 d , the densities of the various phases of the flowing multiphase fluid 101 determined at block 309 d , and the void fraction ( ⁇ g ) determined at block 313 d .
- the density of the liquid phase ( ⁇ l ) can be calculated at block 315 d , for example, by Equation 6e.
- ⁇ l ⁇ app - ⁇ g ⁇ ⁇ g 1 - ⁇ g ( 6 ⁇ e )
- a mixture density ( ⁇ ) of the multiphase fluid 101 is calculated based on the density of the gas phase ( ⁇ g ) determined at block 309 d , the gas phase volume fraction ( ⁇ g ) determined at block 311 d , and the density of the liquid phase ( ⁇ l ) determined at block 315 d .
- the mixture density ( ⁇ ) can be determined at block 317 c by Equation 6d.
- a total mass flow rate (m T ) of the multiphase fluid 101 is determined.
- the total mass flow rate (m T ) can be determined, for example, by a mass flowmeter and/or by any of Equations 3a, 4a, or 4b.
- the blocks in the dotted box of the multiphase fluid flow model 300 D (blocks 313 d , 315 d , 317 d , determining the total mass flow rate (m T ), and determining the slip ratio (S)) are performed simultaneously (for example, in parallel).
- the blocks in the dotted box of the multiphase fluid flow model 300 D are performed iteratively (for example, in series) until the calculated values converge to final values.
- a water-liquid ratio (R WL ) of the multiphase fluid 101 is determined.
- the water-liquid ratio (R WL ) can be determined at block 319 d by re-arranging Equation 6c to solve for R WL
- FIG. 3 E is a flowchart depicting an example multiphase fluid flow model 300 E.
- Any one of the apparatuses 100 E, 100 F, 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 E to characterize a multiphase fluid, such as the multiphase fluid 101 .
- a first differential pressure ( ⁇ P 1 ) and a second differential pressure ( ⁇ P 2 ) of the flowing multiphase fluid 101 is measured.
- the first differential pressure ( ⁇ P 1 ) is measured across a first bend in piping.
- the second differential pressure ( ⁇ P 2 ) is measured across a second bend in piping.
- the multiphase fluid 101 flows generally upward across either of the first or second bends and flows generally downward across the other of the first or second bends.
- the multiphase fluid 101 flows generally upward across the first bend and flows generally downward across the second bend.
- the multiphase fluid 101 flows generally downward across the first bend and flows generally upward across the second bend. Examples are provided with respect to apparatuses 100 E, 100 F, 100 H, 100 I, and 100 J shown in FIGS. 1 E, 1 F, 1 H, 1 I, and 1 J , respectively).
- either one of the first differential pressure ( ⁇ P 1 ) or the second differential pressure ( ⁇ P 2 ) measured at block 301 e is selected for further calculations in the model 300 E.
- a void fraction ( ⁇ g ) of the multiphase fluid 101 is determined.
- the void fraction ( ⁇ g ) determined at block 305 e can be measured for example, by an external sensor (such as an ultrasonic sensor).
- various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowing multiphase fluid 101 are determined.
- the conditions and/or properties determined at block 307 e can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers).
- a water-liquid ratio (R WL ) of the flowing multiphase fluid 101 is determined.
- the water-liquid ratio (R WL ) can be determined at block 309 e can be measured, for example, by external sensors (such as dynamic pressure sensors, as in apparatus 100 G shown in FIG. 1 G ).
- densities of the various phases (such as density of the gas phase ( ⁇ g ), density of the aqueous phase ( ⁇ a ), and density of the oil phase ( ⁇ o )) of the flowing multiphase fluid 101 are determined.
- the densities of the various phases of the flowing multiphase fluid 101 can be determined at block 311 e , for example, based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 307 e .
- a density of the liquid phase ( ⁇ l , including the aqueous phase and the oil phase) is determined.
- the density of the liquid phase ( ⁇ l ) can be determined at block 311 e based on the densities of the various phases of the flowing multiphase fluid 101 and the water-liquid ratio (R WL ) determined at block 309 e .
- the density of the liquid phase ( ⁇ l ) can be determined at block 311 e by Equation 6c.
- the void fraction ( ⁇ g ) can be calculated at block 305 e based on the density of the liquid phase ( ⁇ l ) and the density of the gas phase ( ⁇ g ) determined at block 311 e.
- a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the void fraction ( ⁇ g ) determined at block 305 e and slip ratio (S) of the flowing multiphase fluid 101 .
- the slip ratio (S) used at block 313 e to determine the gas phase volume fraction ( ⁇ g ) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess.
- a mixture density ( ⁇ ) of the multiphase fluid 101 is calculated based on the gas phase volume fraction ( ⁇ g ) determined at block 313 e , the density of the gas phase ( ⁇ g ) determined at block 311 e , and the density of the liquid phase ( ⁇ l ) determined at block 311 e .
- the mixture density ( ⁇ ) can be determined at block 315 e by Equation 6d.
- a total mass flow rate (m T ) of the multiphase fluid 101 is determined.
- the total mass flow rate (m T ) can be determined at block 317 e , for example, by a mass flowmeter and/or by any of Equations 4a or 4b based on the selected differential pressure at block 303 e .
- the blocks in the dotted box of the multiphase fluid flow model 300 E (blocks 313 e , 315 e , 317 e , and determining the slip ratio (S)) are performed simultaneously (for example, in parallel).
- the blocks in the dotted box of the multiphase fluid flow model 300 E (blocks 313 e , 315 e , 317 e , and determining the slip ratio (S)) are performed iteratively (for example, in series) until the calculated values converge to final values.
- FIG. 3 F is a flowchart depicting an example multiphase fluid flow model 300 F.
- Any one of the apparatuses 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 F to characterize a multiphase fluid, such as the multiphase fluid 101 .
- a first differential pressure ( ⁇ P 1 ) and a second differential pressure ( ⁇ P 2 ) of the flowing multiphase fluid 101 is measured.
- the first differential pressure ( ⁇ P 1 ) is measured across a first bend in piping.
- the second differential pressure ( ⁇ P 2 ) is measured across a second bend in piping.
- the multiphase fluid 101 flows generally upward across either of the first or second bends and flows generally downward across the other of the first or second bends.
- the multiphase fluid 101 flows generally upward across the first bend and flows generally downward across the second bend.
- the multiphase fluid 101 flows generally downward across the first bend and flows generally upward across the second bend. Examples are provided with respect to apparatuses 100 E, 100 F, 100 H, 100 I, and 100 J shown in FIGS. 1 E, 1 F, 1 H, 1 I, and 1 J , respectively).
- a third differential pressure ( ⁇ P 3 ) and a fourth differential pressure ( ⁇ P 4 ) of the flowing multiphase fluid 101 is measured.
- the third differential pressure ( ⁇ P 1 ) is measured in a first direction across a specified differential pressure height (h).
- the second differential pressure ( ⁇ P 2 ) is measured in a second direction (different from the first direction) across the specified differential pressure height (h).
- the first and second directions are such that the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction.
- the multiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction.
- the multiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction.
- a frictional pressure loss ( ⁇ P f ) of the flowing multiphase fluid 101 is calculated based on the third and fourth differential pressures ( ⁇ P 3 , ⁇ P 4 ) measured at block 303 f .
- the frictional pressure loss ( ⁇ P f ) can be calculated at block 305 f , for example, by Equation 2h.
- an apparent mixture density ( ⁇ app ) of the multiphase fluid 101 is estimated based on the third and fourth differential pressures ( ⁇ P 3 , ⁇ P 4 ) measured at block 303 f .
- the apparent mixture density ( ⁇ app ) can be estimated at block 307 f , for example, by Equation 2d.
- a void fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the apparent mixture density ( ⁇ app ) estimated at block 307 f .
- the void fraction ( ⁇ g ) can be calculated at block 309 f , for example, by Equation 6b.
- various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowing multiphase fluid 101 are determined.
- the conditions and/or properties determined at block 311 f can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers).
- a water-liquid ratio (R WL ) of the flowing multiphase fluid 101 is determined.
- the water-liquid ratio (R WL ) can be determined at block 313 f can be measured, for example, by external sensors (such as dynamic pressure sensors, as in apparatus 100 G shown in FIG. 1 G ).
- densities of the various phases (such as density of the gas phase ( ⁇ g ), density of the aqueous phase ( ⁇ a ), and density of the oil phase ( ⁇ o )) of the flowing multiphase fluid 101 are determined.
- the densities of the various phases of the flowing multiphase fluid 101 can be determined at block 315 f , for example, based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 311 f .
- a density of the liquid phase ( ⁇ l , including the aqueous phase and the oil phase) is determined.
- the density of the liquid phase ( ⁇ l ) can be determined at block 315 f based on the densities of the various phases of the flowing multiphase fluid 101 and the water-liquid ratio (R WL ) determined at block 313 f .
- the density of the liquid phase ( ⁇ l ) can be determined at block 315 f by Equation 6c.
- the void fraction ( ⁇ g ) can be calculated at block 309 f based on the density of the liquid phase ( ⁇ l ) and the density of the gas phase ( ⁇ g ) determined at block 315 f.
- a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the void fraction ( ⁇ g ) determined at block 309 f and slip ratio (S) of the flowing multiphase fluid 101 .
- the slip ratio (S) used at block 317 f to determine the gas phase volume fraction ( ⁇ g ) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess.
- a mixture density ( ⁇ ) of the multiphase fluid 101 is calculated based on the gas phase volume fraction ( ⁇ g ) determined at block 317 f , the density of the gas phase ( ⁇ g ) determined at block 315 f , and the density of the liquid phase ( ⁇ l ) determined at block 315 f .
- the mixture density ( ⁇ ) can be determined at block 319 f by Equation 6d.
- a friction factor (f d ) of the flowing multiphase fluid 101 is determined based on the frictional pressure loss ( ⁇ P f ) determined at block 305 f .
- a horizontal flow dynamic pressure (q h ) and a vertical flow dynamic pressure (q v ) are determined.
- the horizontal flow dynamic pressure (q h ) and the vertical flow dynamic pressure (q v ) determined at block 323 f can be, for example, measured by external sensors (such as dynamic pressure sensors).
- the horizontal flow dynamic pressure (q h ) is determined by Equation 6f h .
- the vertical flow dynamic pressure (q v ) is determined by Equation 6f v .
- the friction factor (f d ) is determined at block 321 f by Equation 6g, which depends on the horizontal flow dynamic pressure (q h ) and the vertical flow dynamic pressure (q v ) determined at block 323 f (for example, by sensors or by Equations 6f h and 6f v .
- Equation 6f h is a cross-sectional flow area for the horizontal flow of the multiphase fluid 101 .
- a v is a cross-sectional flow area for the vertical flow of the multiphase fluid 101 .
- Equation 6g h is the specified differential pressure height, and D v is the inner diameter of the conduit in which the direction of flow of the multiphase fluid 101 is generally upward or generally downward.
- a total mass flow rate (m T ) of the multiphase fluid 101 is determined.
- the total mass flow rate (m T ) can be determined at block 325 f , for example, by a mass flowmeter and/or by any of Equations 4a or 4b.
- the total mass flow rate (m T ) can be determined at block 325 f based on the first and second differential pressures ( ⁇ P 1 , ⁇ P 2 ) measured at block 301 f , the mixture density ( ⁇ ) determined at block 319 f , the friction factor (f d ) determined at block 321 f , and the horizontal and vertical flow dynamic pressures (q h , q v ) determined at block 323 f .
- the total mass flow rate (m T ) is determined at block 325 f by Equation 6h.
- C d is an empirically characterized discharge coefficient
- ⁇ is an expansion factor
- ⁇ P L is the differential pressure across the bend (selected from one of the first or second differential pressures ( ⁇ P 1 or ⁇ P 2 ))
- g is the acceleration due to gravity
- y is the vertical height difference between the pressure ports for the differential pressure sensor
- x is the horizontal distance between the pressure ports for the differential pressure sensor
- D′ h is the equivalent (effective) inner diameter of the cross-sectional flow area for the horizontal flow of the multiphase fluid 101
- D′ v is the equivalent (effective) inner diameter of the cross-sectional flow area for the vertical flow of the multiphase fluid 101 .
- the blocks in the dotted box of the multiphase fluid flow model 300 F are performed simultaneously (for example, in parallel). In some implementations, the blocks in the dotted box of the multiphase fluid flow model 300 F (blocks 317 f , 319 f , 321 f , 323 f , 325 f , and determining the slip ratio (S)) are performed iteratively (for example, in series) until the calculated values converge to final values.
- various volumetric flow rates of the multiphase fluid 101 are determined.
- the various volumetric flow rates determined at block 327 f can include a total volumetric flow rate (Q T ) of the multiphase fluid 101 , a gas phase volumetric flow rate (Q g ) of the multiphase fluid 101 , a liquid phase volumetric flow rate (Q l , including the aqueous phase and the oil phase) of the multiphase fluid 101 , an oil phase volumetric flow rate (Q o ) of the multiphase fluid 101 , and an aqueous phase volumetric flow rate (Q a ) of the multiphase fluid 101 .
- the various volumetric flow rates determined at block 327 f can be calculated by Equations 6j t , 6j g , 6j l , 6j o , and 6j a .
- FIG. 3 G is a flowchart depicting an example multiphase fluid flow model 300 G.
- Any one of the apparatuses 100 H, 100 I, or 100 J can, for example, be used to implement the model 300 G to characterize a multiphase fluid, such as the multiphase fluid 101 .
- various operating conditions (such as pressure and temperature) about the flowing multiphase fluid 101 are determined.
- the various operating conditions determined at block 301 g can be measured, for example, by external sensors, such as pressure sensors and temperature sensors.
- the various operating conditions determined at block 301 g can include, for example, differential pressure measurements.
- a salinity of the aqueous phase of the multiphase fluid 101 is measured.
- the salinity of the aqueous phase of the multiphase fluid 101 can be measured at block 303 g , for example, using a salinity sensor.
- the salinity sensor includes electrodes for generating a current to measure conductivity of the aqueous phase of the multiphase fluid 101 .
- fluid properties (such as density) of the various phases (such as the gas phase, the aqueous phase, and the oil phase) of the multiphase fluid 101 are determined.
- the fluid properties of the various phases can be determined at block 305 g based on the operating conditions measured at block 301 g and the salinity of the aqueous phase measured at block 303 g .
- a void fraction ( ⁇ g ) of the multiphase fluid 101 is determined.
- the void fraction ( ⁇ g ) can be determined at block 307 g , for example, using an external sensor (such as an ultrasonic sensor) and/or by Equation 6b.
- a water-liquid ratio (R WL ) of the multiphase fluid 101 is determined.
- the water-liquid ratio (R WL ) can be determined at block 309 g , for example, using an external sensor (such as a dynamic pressure sensor).
- a density of the liquid phase ( ⁇ l , including the aqueous phase and the oil phase) is determined.
- the density of the liquid phase ( ⁇ l ) can be determined at block 311 g based on the densities of the various phases of the flowing multiphase fluid 101 and the water-liquid ratio (R WL ) determined at block 309 g .
- the density of the liquid phase ( ⁇ l ) can be determined at block 311 g , for example, by Equation 6c.
- a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 is calculated based on the void fraction ( ⁇ g ) determined at block 307 g and slip ratio (S) of the flowing multiphase fluid 101 .
- the slip ratio (S) used at block 313 g to determine the gas phase volume fraction ( ⁇ g ) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess.
- a mixture density ( ⁇ ) of the multiphase fluid 101 is calculated based on the gas phase volume fraction ( ⁇ g ) determined at block 313 g , the density of the gas phase ( ⁇ g ) determined at block 305 g , and the density of the liquid phase ( ⁇ l ) determined at block 311 g .
- the mixture density ( ⁇ ) can be determined at block 315 g , for example, by Equation 6d.
- a total mass flow rate (m T ) of the multiphase fluid 101 is determined.
- the total mass flow rate (m T ) can be determined at block 317 g , for example, by a mass flowmeter and/or by any of Equations 4a or 4b.
- the blocks in the dotted box of the multiphase fluid flow model 300 G are performed simultaneously (for example, in parallel). In some implementations, the blocks in the dotted box of the multiphase fluid flow model 300 G (blocks 313 g , 315 g , 317 g , and determining the slip ratio (S)) are performed iteratively (for example, in series) until the calculated values converge to final values.
- various volumetric flow rates of the multiphase fluid 101 are determined.
- the various volumetric flow rates determined at block 319 g can include a total volumetric flow rate (Q T ) of the multiphase fluid 101 , a gas phase volumetric flow rate (Q g ) of the multiphase fluid 101 , a liquid phase volumetric flow rate (Q l , including the aqueous phase and the oil phase) of the multiphase fluid 101 , an oil phase volumetric flow rate (Q o ) of the multiphase fluid 101 , and an aqueous phase volumetric flow rate (Q a ) of the multiphase fluid 101 .
- the various volumetric flow rates determined at block 319 g can be calculated by Equations 6j t , 6j g , 6j l , 6j o , and 6j a .
- FIG. 4 is a flowchart of an example method 400 for measuring a density of a multiphase fluid 101 .
- Any one of the apparatuses 100 A, 100 B, 100 C, 100 D, 100 H, 100 I, or 100 J can be used, for example, to implement the method 400 .
- a multiphase fluid (such as the multiphase fluid 101 ) is flowed through a U-bend (such as the U-bend 102 ).
- the multiphase fluid 101 can include a gas phase 101 a , an aqueous phase 101 b ′, and an oil phase 101 b ′′.
- the U-bend 102 includes a first conduit 102 a , a second conduit 102 b , and a connecting conduit 102 c .
- the first conduit 102 a is parallel to the second conduit 102 b .
- the connecting conduit 102 c connects the second conduit 102 b to the first conduit 102 a .
- Each of the first conduit 102 a , the second conduit 102 b , and the connecting conduit 102 c have substantially the same cross-sectional flow area for the multiphase fluid 101 flowing through the U-bend 102 .
- the multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102 a , through the connecting conduit 102 c , and out of the second conduit 102 b .
- a first differential pressure ( ⁇ P 1 ) of the multiphase fluid 101 is measured across a specified differential pressure height (h) along the first conduit 102 a .
- the first differential pressure ( ⁇ P 1 ) of the multiphase fluid 101 can be measured at block 404 , for example, by the first pair of pressure sensors 104 a , 104 b .
- a second differential pressure ( ⁇ P 2 ) of the multiphase fluid 101 is measured across the specified differential pressure height (h) along the second conduit 102 b .
- the second differential pressure ( ⁇ P 2 ) of the multiphase fluid 101 can be measured at block 406 , for example, by the second pair of pressure sensors 104 c , 104 d .
- a mixture density ( ⁇ ) of the multiphase fluid 101 is determined at least based on a difference between the first differential pressure ( ⁇ P 1 ) and the second differential pressure ( ⁇ P 2 ) of the multiphase fluid 101 (measured at blocks 404 and 406 , respectively) and the specified differential pressure height (h).
- the mixture density ( ⁇ ) of the multiphase fluid 101 can be determined at block 406 using Equation 2d.
- the method 400 includes determining an aqueous phase volume fraction ( ⁇ a ) of the multiphase fluid 101 at least based on the gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 , the gas density ( ⁇ g ) of the gas phase 101 a of the multiphase fluid 101 , the aqueous phase density ( ⁇ a ) of the aqueous phase 101 b ′ of the multiphase fluid 101 , the oil phase density ( ⁇ o ) of the oil phase 101 b ′′ of the multiphase fluid 101 , and the mixture density ( ⁇ ) of the multiphase fluid 101 .
- the gas phase volume fraction ( ⁇ g ), the gas density ( ⁇ g ), the aqueous phase density ( ⁇ a ), the oil phase density ( ⁇ o ), and the mixture density ( ⁇ ) of the multiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the aqueous phase volume fraction ( ⁇ a ) of the multiphase fluid 101 .
- the method 400 includes determining a gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 at least based on the aqueous phase volume fraction ( ⁇ a ) of the multiphase fluid 101 , the gas density ( ⁇ g ) of the gas phase 101 a of the multiphase fluid 101 , the aqueous phase density ( ⁇ a ) of the aqueous phase 101 b ′ of the multiphase fluid 101 , the oil phase density ( ⁇ o ) of the oil phase 101 b ′′ of the multiphase fluid 101 , and the mixture density ( ⁇ ) of the multiphase fluid 101 .
- the aqueous phase volume fraction ( ⁇ a ), the gas density ( ⁇ g ), the aqueous phase density ( ⁇ a ), the oil phase density ( ⁇ o ), and the mixture density ( ⁇ ) of the multiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the gas phase volume fraction ( ⁇ g ) of the multiphase fluid 101 .
- FIG. 5 is a flowchart of an example method 500 for measuring a total flow rate of a multiphase fluid 101 .
- Any one of the apparatuses 100 E, 100 H, 100 I, or 100 J can be used, for example, to implement the method 500 .
- a multiphase fluid (such as the multiphase fluid 101 ) is flowed from a flow pipe (such as the flow pipe 150 ) to a U-bend (such as the U-bend 102 ).
- the multiphase fluid 101 can include a gas phase 101 a , an aqueous phase 101 b ′, and an oil phase 101 b ′′.
- the U-bend 102 includes a first conduit 102 a , a second conduit 102 b , and a connecting conduit 102 c .
- the connecting conduit 102 c connects the first conduit 102 a to the second conduit 102 b .
- the multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102 a , through the connecting conduit 102 c , and out of the second conduit 102 b .
- the flow pipe 150 includes the first pipe 150 a (third conduit) and the second pipe 150 b (fourth conduit).
- the first pipe 150 a is connected to the first conduit 102 a of the U-bend 102 by a first bend (such as the first angled bend 153 a ).
- the second pipe 150 b is connected to the second conduit 102 b of the U-bend 102 by a second bend (such as the second angled bend 153 b ).
- Flowing the multiphase fluid 101 from the flow pipe 150 to the U-bend 102 at block 502 includes flowing the multiphase fluid 101 from the first pipe 150 a of the flow pipe 150 through the first angled bend 153 a to the first conduit 102 a of the U-bend 102 .
- the multiphase fluid 101 is flowed from the U-bend 102 to the flow pipe 150 .
- Flowing the multiphase fluid 101 from the U-bend 102 to the flow pipe 150 at block 504 includes flowing the multiphase fluid 101 from the second conduit 102 b of the U-bend 102 through the second angled bend 153 b to the second pipe 150 b of the flow pipe 150 .
- a first differential pressure of the multiphase fluid 101 is measured between a first location on the first pipe 150 a of the flow pipe 150 and a second location on the first conduit 102 a of the U-bend 102 .
- the first differential pressure of the multiphase fluid 101 can be measured at block 506 cooperatively by the first pressure sensor 104 a coupled to the first pipe 150 a of the flow pipe 150 at the first location and by the second pressure sensor 104 b coupled to the first conduit 102 a of the U-bend at the second location.
- a second differential pressure of the multiphase fluid 101 is measured between a third location on the second conduit 102 b of the U-bend 102 and a fourth location on the second pipe 150 b of the flow pipe 150 .
- the second differential pressure of the multiphase fluid 101 can be measured at block 508 cooperatively by the third pressure sensor 104 c coupled to the second conduit 102 b of the U-bend 102 at the third location and by the fourth pressure sensor 104 d coupled to the second pipe 150 b of the flow pipe 150 at the fourth location.
- an overall flow rate of the multiphase fluid 101 is determined at least based on the first differential pressure (measured at block 506 ), the second differential pressure (measured at block 508 ), a difference between the first differential pressure and the second differential pressure, and an overall density of the multiphase fluid 101 .
- the total mass flow rate (m T1 ) of the multiphase fluid 101 can be determined at block 510 using Equation 4a.
- the total mass flow rate (m T2 ) of the multiphase fluid 101 can be determined at block 510 using Equation 4b.
- the method 500 includes comparing the total flow rates (m T1 , m T2 ) of the multiphase fluid 101 determined at block 510 (for example, determined by Equations 4a and 4b) to determine an adjustment of the discharge coefficients (for example, C d1 , C d2 ).
- FIG. 6 is a flowchart of an example method 600 for measuring a mixture density, a total flow rate, and phase flow rates of a multiphase fluid 101 .
- Any of the apparatuses 100 H, 100 I, or 100 J can be used, for example, to implement the method 600 .
- a multiphase fluid (such as the multiphase fluid 101 ) is flowed from a flow pipe (such as the flow pipe 150 ) to a U-bend (such as the U-bend 102 ).
- the multiphase fluid 101 can include a gas phase 101 a , an aqueous phase 101 b ′, and an oil phase 101 b ′′.
- the U-bend 102 includes a first conduit 102 a , a second conduit 102 b , and a connecting conduit 102 c .
- the connecting conduit 102 c connects the first conduit 102 a to the second conduit 102 b .
- the multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102 a , through the connecting conduit 102 c , and out of the second conduit 102 b .
- the flow pipe 150 includes the first pipe 150 a (third conduit) and the second pipe 150 b (fourth conduit).
- the first pipe 150 a is connected to the first conduit 102 a of the U-bend 102 by a first bend (such as the first angled bend 153 a ).
- the second pipe 150 b is connected to the second conduit 102 b of the U-bend 102 by a second bend (such as the second angled bend 153 b ).
- Flowing the multiphase fluid 101 from the flow pipe 150 to the U-bend 102 at block 602 includes flowing the multiphase fluid 101 from the first pipe 150 a of the flow pipe 150 through the first angled bend 153 a to the first conduit 102 a of the U-bend 102 .
- the multiphase fluid 101 is flowed from the U-bend 102 to the flow pipe 150 .
- Flowing the multiphase fluid 101 from the U-bend 102 to the flow pipe 150 at block 604 includes flowing the multiphase fluid 101 from the second conduit 102 b of the U-bend 102 through the second angled bend 153 b to the second pipe 150 b of the flow pipe 150 .
- a first differential pressure of the multiphase fluid 101 is measured between a first location on the first pipe 150 a of the flow pipe 150 and a second location on the first conduit 102 a of the U-bend 102 .
- the first differential pressure of the multiphase fluid 101 can be measured at block 606 cooperatively by the first pressure sensor 104 a coupled to the first pipe 150 a of the flow pipe 150 at the first location and by the second pressure sensor 104 b coupled to the first conduit 102 a of the U-bend at the second location.
- a second differential pressure of the multiphase fluid 101 is measured between a third location on the second conduit 102 b of the U-bend 102 and a fourth location on the second pipe 150 b of the flow pipe 150 .
- the second differential pressure of the multiphase fluid 101 can be measured at block 608 cooperatively by the third pressure sensor 104 c coupled to the second conduit 102 b of the U-bend 102 at the third location and by the fourth pressure sensor 104 d coupled to the second pipe 150 b of the flow pipe 150 at the fourth location.
- a third differential pressure of the multiphase fluid 101 is measured across a specified height (such as the specified height, h) along the longitudinal length of the first conduit 102 a of the U-bend 102 .
- the third differential pressure of the multiphase fluid 101 can be measured at block 610 by the third pair of pressure sensors 104 e , 104 f coupled to the first conduit 102 a .
- a fourth differential pressure of the multiphase fluid 101 is measured across the specified height (h) along the longitudinal length of the second conduit 102 b of the U-bend 102 .
- the fourth differential pressure of the multiphase fluid 101 can be measured at block 612 by the fourth pair of pressure sensors 104 g , 104 h coupled to the second conduit 102 b .
- a mixture density ( ⁇ ) of the multiphase fluid 101 is determined at least based on a difference between the third differential pressure ( ⁇ P 3 ) and the fourth differential pressure ( ⁇ P 4 ) of the multiphase fluid 101 (measured at blocks 610 and 612 , respectively) and the specified height (h).
- the mixture density ( ⁇ ) of the multiphase fluid 101 can be determined at block 614 using Equation 2d, where ⁇ P 1 is substituted for the third differential pressure ( ⁇ P 3 ) measured by the third pair of pressure sensors 104 e , 104 f at block 610 , ⁇ P 2 is substituted for the fourth differential pressure ( ⁇ P 4 ) measured by the fourth pair of pressure sensors 104 g , 104 h at block 612 , and h 2 is substituted for the specified height (h).
- a total flow rate of the multiphase fluid 101 is determined at least based on the first differential pressure (measured at block 606 ), the second differential pressure (measured at block 608 ), and a mixture density of the multiphase fluid 101 (determined at block 614 ).
- the total mass flow rate (m T1 ) of the multiphase fluid 101 can be determined at block 616 using Equation 4a.
- the total mass flow rate (m T2 ) of the multiphase fluid 101 can be determined at block 616 using Equation 4b.
- the method 600 includes comparing the total flow rates (m T1 , m T2 ) of the multiphase fluid 101 determined at block 616 (for example, determined by Equations 4a and 4b) to determine an adjustment of the discharge coefficients (C d1 , C d2 ).
- the method 600 can include measuring various dynamic pressures of the multiphase fluid 101 flowing through the U-bend 102 .
- the dynamic pressures of the multiphase fluid 101 can be measured, for example, by the dynamic pressure sensors 106 a , 106 b , 106 c .
- the dynamic pressure measurements taken by the dynamic pressure sensors 106 a , 106 b , 106 c can be cross-correlated (for example, by the processor 705 ) to determine a speed of sound of the multiphase fluid 101 flowing through the U-bend 102 .
- the speed of sound of the multiphase fluid 101 and the mixture density ( ⁇ ) of the multiphase fluid 101 can then be used to determine the water-liquid ratio of the multiphase fluid 101 .
- the speed of sound of the multiphase fluid 101 and the mixture density ( ⁇ ) of the multiphase fluid 101 can be compared to a plotted graph of various phase curves (gas/oil, gas/aqueous, oil/aqueous) to determine the water-liquid ratio.
- FIG. 7 is a block diagram of an example computer 700 used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures, as described in this specification, according to an implementation.
- the illustrated computer 700 is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, one or more processors within these devices, or any other processing device, including physical or virtual instances (or both) of the computing device.
- the computer 700 can include a computer that includes an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer 700 , including digital data, visual, audio information, or a combination of information.
- the computer 700 includes an interface 704 . Although illustrated as a single interface 704 in FIG. 7 , two or more interfaces 704 may be used according to particular needs, desires, or particular implementations of the computer 700 . Although not shown in FIG. 7 , the computer 700 can be communicably coupled with a network.
- the interface 704 is used by the computer 700 for communicating with other systems that are connected to the network in a distributed environment.
- the interface 704 comprises logic encoded in software or hardware (or a combination of software and hardware) and is operable to communicate with the network. More specifically, the interface 704 may comprise software supporting one or more communication protocols associated with communications such that the network or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer 700 .
- the interface 704 can include a control interface, which can be used to couple the computer 700 to controls.
- the control interface is a bank of relays, a bank of MOSFET power controllers, a serial peripheral interface (SPI), or a Fieldbus, and the like.
- the interface 704 can include a sensor interface, which can be used to couple the computer 700 to sensors.
- the sensor interface is a bank of analog-to-digital converters (ADCs), and I2C bus, a serial peripheral interface (SPI) bus, or a Fieldbus, and the like.
- the interface 704 can include a human machine interface, which can be used by a user to interact with the computer 700 .
- the human machine interface includes a monitor or a touch screen that is configured to display information, for example, to a user.
- the computer 700 includes a processor 705 .
- the processor 705 may be a microprocessor, a multi-core processor, a multithreaded processor, an ultra-low-voltage processor, an embedded processor, or a virtual processor.
- the processor 705 may be part of a system-on-a-chip (SoC) in which the processor 705 and the other components of the computer 700 are formed into a single integrated electronics package.
- SoC system-on-a-chip
- the processor 705 may include processors from Intel® Corporation of Santa Clara, California, from Advanced Micro Devices, Inc. (AMD) of Sunnyvale, California, or from ARM Holdings, LTD., Of Cambridge, England. Any number of other processors from other suppliers may also be used. Although illustrated as a single processor 705 in FIG.
- processors may be used according to particular needs, desires, or particular implementations of the computer 700 .
- the processor 705 executes instructions and manipulates data to perform the operations of the computer 700 and any algorithms, methods, functions, processes, flows, and procedures as described in this specification.
- the processor 705 may communicate with other components of the computer 700 over a bus.
- the bus may include any number of technologies, such as industry standard architecture (ISA), extended ISA (EISA), peripheral component interconnect (PCI), peripheral component interconnect extended (PCIx), PCI express (PCIe), or any number of other technologies.
- the bus may be a proprietary bus, for example, used in an SoC based system. Other bus technologies may be used, in addition to, or instead of, the technologies above.
- the computer 700 can also include a database 706 that can hold data for the computer 700 or other components (or a combination of both) that can be connected to the network.
- a database 706 that can hold data for the computer 700 or other components (or a combination of both) that can be connected to the network.
- database 706 can be used according to particular needs, desires, or particular implementations of the computer 700 and the described functionality.
- database 706 is illustrated as an integral component of the computer 700
- database 706 can be external to the computer 700 .
- the database 706 can be used for the persistent storage of information, such as data, applications, operating systems, and so forth.
- the database 706 may be a nonvolatile RAM, a solid-state disk drive, or a flash drive, among others.
- the database 306 will include a hard disk drive, such as a micro hard disk drive, a regular hard disk drive, or an array of hard disk drives, for example, associated with a DCS or a cloud server.
- the computer 700 also includes a memory 707 that can hold data for the computer 700 or other components (or a combination of both) that can be connected to the network. Although illustrated as a single memory 707 in FIG. 7 , two or more memories 707 (of the same or combination of types) can be used according to particular needs, desires, or particular implementations of the computer 700 and the described functionality. While memory 707 is illustrated as an integral component of the computer 700 , memory 707 can be external to the computer 700 .
- the memory 707 can be a transitory or non-transitory storage medium. In some implementations, such as in PLCs and other process control units, the memory 707 is integrated with the database 706 used for long-term storage of programs and data.
- the memory 707 can include any number of volatile and nonvolatile memory devices, such as volatile random-access memory (RAM), static random-access memory (SRAM), flash memory, and the like. In smaller devices, such as PLCs, the memory 707 may include registers associated with the processor 705 itself.
- RAM volatile random-access memory
- SRAM static random-access memory
- flash memory and the like.
- the memory 707 may include registers associated with the processor 705 itself.
- the memory 707 stores computer-readable instructions executable by the processor 705 that, when executed, cause the processor 705 to perform operations, such as receiving a first differential pressure signal from the first pair of pressure sensors 104 a , 104 b ; receiving a second differential pressure signal from the second pair of pressure sensors 104 c , 104 d ; and determining an overall density of the multiphase fluid 101 at least based on a difference between the first differential pressure and the second differential pressure of the multiphase fluid 101 and the specified differential pressure height, h.
- the computer 700 can also include a power supply 714 .
- the power supply 714 can include a rechargeable or non-rechargeable battery that can be configured to be either user- or non-user-replaceable.
- the power supply 714 can be hard-wired.
- computers 700 there may be any number of computers 700 associated with, or external to, a computer system containing computer 700 , each computer 700 communicating over the network. Further, the term “client,” “user,” “operator,” and other appropriate terminology may be used interchangeably, as appropriate, without departing from this specification. Moreover, this specification contemplates that many users may use one computer 700 , or that one user may use multiple computers 700 .
- the terms “a,” “an,” or “the” are used to include one or more than one unless the context clearly dictates otherwise.
- the term “or” is used to refer to a nonexclusive “or” unless otherwise indicated.
- the statement “at least one of A and B” has the same meaning as “A, B, or A and B.”
- the phraseology or terminology employed in this disclosure, and not otherwise defined is for the purpose of description only and not of limitation. Any use of section headings is intended to aid reading of the document and is not to be interpreted as limiting; information that is relevant to a section heading may occur within or outside of that particular section.
- the term “about” or “approximately” can allow for a degree of variability in a value or range, for example, within 10%, within 5%, or within 1% of a stated value or of a stated limit of a range.
- the term “substantially” refers to a majority of, or mostly, as in at least about 50%, 60%, 70%, 80%, 90%, 95%, 96%, 97%, 98%, 99%, 99.5%, 99.9%, 99.99%, or at least about 99.999% or more.
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Abstract
Description
- This disclosure relates to characterization of the flow of multiphase fluids.
- A multiphase fluid is a mixture of multiple phases of matter. Multiphase fluids can be non-homogenous and can thus exhibit complex flow characteristics. The characteristics of the flow of multiphase fluids in a conduit, for example, can depend on various factors, such as operating conditions (pressure and temperature), composition (and in turn, physical properties such as density and viscosity) of each of the phases, flow rate of each of the phases, and physical characteristics of the conduit (such as diameter and orientation) through which the multiphase fluid is flowing. Characterization of the flow of multiphase fluids can sometimes be difficult. In some cases, for example, in oil and gas operations, accurate flow metering of multiphase fluid mixtures (such as crude oil, natural gas, and brine) can be important.
- This disclosure describes technologies relating to measuring density of multiphase fluids. Certain aspects of the subject matter described can be implemented as a system. The system includes a U-bend, a first differential pressure sensor, a second differential pressure sensor, and a computer. The U-bend is configured to flow a multiphase fluid. The U-bend includes a first conduit, a second conduit, and a connecting conduit. The connecting conduit connects the first conduit to the second conduit. Each of the first conduit and the second conduit have substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend. The multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit. The multiphase fluid includes a gas phase, an aqueous phase, and an oil phase. The first differential pressure sensor is coupled to the first conduit. The first differential pressure sensor is configured to measure a first differential pressure of the multiphase fluid flowing through the U-bend across a specified differential pressure height along the first conduit. The second differential pressure is coupled to the second conduit. The second differential pressure sensor is configured to measure a second differential pressure of the multiphase fluid flowing through the U-bend across the specified differential pressure height along the second conduit. The computer includes a processor and a computer-readable storage medium. The processor is communicatively coupled to the first differential pressure sensor and to the second differential pressure sensor. The computer-readable storage medium is coupled to the processor and stores programming instructions for execution by the processor. The programming instructions instruct the processor to perform operations. The operations include receiving a first differential pressure signal from the first differential pressure sensor. The first differential pressure signal represents the first differential pressure of the multiphase fluid. The operations include receiving a second differential pressure signal from the second differential pressure sensor. The second differential pressure signal represents the second differential pressure of the multiphase fluid. The operations include determining a mixture density of the multiphase fluid at least based on the specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid.
- This, and other aspects, can include one or more of the following features.
- In some implementations, the mixture density of the multiphase fluid is determined by:
-
- where ρ is the mixture density of the multiphase fluid, ΔP1 is the first differential pressure of the multiphase fluid, ΔP2 is the second differential pressure of the multiphase fluid, g is an acceleration due to gravity, and h is the specified differential pressure height.
- In some implementations, the operations performed by the processor include determining a total mass flow rate of the multiphase fluid by:
-
m T =C d ×ε×K×√{square root over (2×ρ×(ΔP−k f ×ΔP f))}, - where mT is the total mass flow rate of the multiphase fluid, Cd is a discharge coefficient, ε is an expansion factor, K is a fixed geometry factor related to a cross-sectional flow area of the U-bend, ρ is the mixture density of the multiphase fluid, ΔP is the first differential pressure or the second differential pressure of the multiphase fluid, kf is a geometry-based correction factor for friction, and ΔPf is frictional pressure loss.
- In some implementations, the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit. In some implementations, the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit. In some implementations, the connecting conduit is perpendicular to the first conduit and to the second conduit.
- In some implementations, the operations performed by the processor include receiving, as input, a gas phase volume fraction of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, a gas phase density of a gas phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an aqueous phase density of an aqueous phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an oil phase density of an oil phase of the multiphase fluid. In some implementations, the operations performed by the processor include determining an aqueous phase volume fraction of the multiphase fluid by:
-
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa), - where ρ is the mixture density of the multiphase fluid, αg is the gas phase volume fraction of the multiphase fluid, αα is the aqueous phase volume fraction of the multiphase fluid, ρg is the gas phase density of the gas phase of the multiphase fluid, ρa is the aqueous phase density of the aqueous phase of the multiphase fluid, and ρo is the oil phase density of the oil phase of the multiphase fluid.
- In some implementations, the operations performed by the processor include receiving, as input, an aqueous phase volume fraction of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, a gas phase density of a gas phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an aqueous phase density of an aqueous phase of the multiphase fluid. In some implementations, the operations performed by the processor include receiving, as input, an oil phase density of an oil phase of the multiphase fluid. In some implementations, the operations performed by the processor include determining a gas phase volume fraction of the multiphase fluid by:
-
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa), - where ρ is the mixture density of the multiphase fluid, αg is the gas phase volume fraction of the multiphase fluid, αa is the aqueous phase volume fraction of the multiphase fluid, ρg is the gas phase density of the gas phase of the multiphase fluid, ρa is the aqueous phase density of the aqueous phase of the multiphase fluid, and ρo is the oil phase density of the oil phase of the multiphase fluid.
- Certain aspects of the subject matter described can be implemented as a method. A multiphase fluid is flowed through a U-bend. The multiphase fluid includes a gas phase, an aqueous phase, and an oil phase. The U-bend includes a first conduit, a second conduit, and a connecting conduit. The connecting conduit connects the first conduit to the second conduit. Each of the first conduit and the second conduit have substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend. The multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit. A first differential pressure of the multiphase fluid is measured across a specified differential pressure height along the first conduit. A second differential pressure of the multiphase fluid is measured across the specified differential pressure height along the second conduit. A mixture density of the multiphase fluid is determined at least based on the specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid.
- This, and other aspects, can include one or more of the following features.
- In some implementations, the mixture density of the multiphase fluid is determined by:
-
- where ρ is the mixture density of the multiphase fluid, ΔP1 is the first differential pressure of the multiphase fluid, ΔP2 is the second differential pressure of the multiphase fluid, g is an acceleration due to gravity, and h is the specified differential pressure height.
- In some implementations, a total mass flow rate of the multiphase fluid is determined by:
-
m T =C d ×ε×K×√{square root over (2×ρ×(ΔP−k f ×ΔP f))}, - wherein mT is the total mass flow rate of the multiphase fluid, Cd is a discharge coefficient, ε is an expansion factor, K is a fixed geometry factor related to a cross-sectional flow area of the U-bend, ρ is the mixture density of the multiphase fluid, ΔP is the first differential pressure or the second differential pressure of the multiphase fluid, kf is a geometry-based correction factor for friction, and ΔPf is frictional pressure loss.
- In some implementations, an aqueous phase volume fraction of the multiphase fluid is determined by:
-
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa), - where ρ is the mixture density of the multiphase fluid, αg is a gas phase volume fraction of the multiphase fluid, αa is an aqueous phase volume fraction of the multiphase fluid, ρg is a gas phase density of the gas phase of the multiphase fluid, ρa is an aqueous phase density of the aqueous phase of the multiphase fluid, and ρo is an oil phase density of the oil phase of the multiphase fluid.
- In some implementations, a gas phase volume fraction of the multiphase fluid is determined by:
-
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa), - where ρ is the mixture density of the multiphase fluid, αg is a gas phase volume fraction of the multiphase fluid, αa is an aqueous phase volume fraction of the multiphase fluid, ρg is a gas phase density of the gas phase of the multiphase fluid, ρa is an aqueous phase density of the aqueous phase of the multiphase fluid, and ρo is an oil phase density of the oil phase of the multiphase fluid.
- In some implementations, the first differential pressure of the multiphase fluid is measured by a first differential pressure sensor coupled to the first conduit. In some implementations, the second differential pressure of the multiphase fluid is measured by a second differential pressure sensor coupled to the second conduit. In some implementations, the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit. In some implementations, the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.
- The details of one or more implementations of the subject matter of this disclosure are set forth in the accompanying drawings and the description. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.
-
FIG. 1A is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid. -
FIG. 1B is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid. -
FIG. 1C is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid. -
FIG. 1D is a schematic diagram of an example apparatus which can be used to measure a density of a multiphase fluid. -
FIG. 1E is a schematic diagram of an example apparatus which can be used to measure a flow rate of a multiphase fluid. -
FIG. 1F is a schematic diagram of an example apparatus which can be used to measure a flow rate of a multiphase fluid. -
FIG. 1G is a schematic diagram of an example apparatus which can be used to measure a water-liquid ratio of a multiphase fluid. -
FIG. 1H is a schematic diagram of an example apparatus which can be used to measure a density and a flow rate of a multiphase fluid. -
FIG. 1I is a schematic diagram of an example apparatus which can be used to measure a density, a flow rate, and a water-liquid ratio of a multiphase fluid. -
FIG. 1J is a schematic diagram of an example apparatus which can be used to measure a density, a flow rate, and a water-liquid ratio of a multiphase fluid. -
FIG. 2A is a schematic diagram depicting various example pressure tap arrangements. -
FIG. 2B is a schematic diagram depicting various example piping arrangements. -
FIG. 2C is a schematic diagram depicting various example piping arrangements. -
FIG. 2D is a schematic diagram depicting various example piping arrangements. -
FIG. 2E is a schematic diagram depicting various example piping arrangements. -
FIG. 2F is a schematic diagram depicting various example sensor arrangements. -
FIG. 3A is a flowchart depicting an example multiphase fluid flow model. -
FIG. 3B is a flowchart depicting an example multiphase fluid flow model for determining density. -
FIG. 3C is a flowchart depicting an example multiphase fluid flow model for determining density. -
FIG. 3D is a flowchart depicting an example multiphase fluid flow model for determining density. -
FIG. 3E is a flowchart depicting an example multiphase fluid flow model for determining flow rate. -
FIG. 3F is a flowchart depicting an example multiphase fluid flow model. -
FIG. 3G is a flowchart depicting an example multiphase fluid flow model. -
FIG. 4 is a flowchart of an example method for measuring a density of a multiphase fluid. -
FIG. 5 is a flowchart of an example method for measuring a flow rate of a multiphase fluid. -
FIG. 6 is a flowchart of an example method for measuring a density and a flow rate of a multiphase fluid. -
FIG. 7 is a block diagram of an example computer system. - This disclosure describes density measurement of multiphase fluids. The apparatuses described here can be used to accurately measure the mixture density of multiphase fluids. The mixture density can then be used to determine other properties of the multiphase fluid, for example, based on additional known information. The apparatuses include multiple connected conduits including an elbow (or L-bend) and a U-bend. The apparatuses include multiple pressure sensors for measuring differential pressures across various location pairs of the flowing multiphase fluid. The measured differential pressures can be compared and manipulated to determine the mixture density of the flowing multiphase fluid.
- The subject matter described in this disclosure can be implemented in particular implementations, so as to realize one or more of the following advantages. The apparatuses, systems, and methods described here can be implemented independent of the use of radioactive energy sources (such as gamma-ray attenuation), which can be hazardous. The apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, even in situations in which a gas phase is present in a non-negligible amount. The apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, while taking into account frictional and shear pressure losses of the multiphase fluid. The apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, even in complex flow regimes such as slug-flow, plug-flow, and annular flow regimes. The apparatuses, systems, and methods described here can be implemented to accurately determine the mixture density of a multiphase fluid, even in situations in which there is slip (that is, differential flow velocity) between gas and liquid phases. The apparatuses, systems, and methods described here can take advantage of pipe geometry (and associated fluid dynamics) to measure a relatively simple (and more direct) flow/fluid property (such as differential pressure), rather than a relatively complex (and more indirect) fluid/flow property (such as electromagnetic (spectral) absorption/transmission) to accurately determine the mixture density of a multiphase fluid. The apparatuses, systems, and methods described here can be implemented in conjunction with other flow metering components to supplement and/or enhance the accuracy of the characterization of multiphase fluid flow.
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FIG. 1A depicts anapparatus 100A which can be used to measure a density of amultiphase fluid 101. Themultiphase fluid 101 can be a 2-phase or a 3-phase fluid. For example, themultiphase fluid 101 can include agas phase 101 a and aliquid phase 101 b. In some implementations, theliquid phase 101 b includes anaqueous phase 101 b′ and anoil phase 101 b″. For example, themultiphase fluid 101 can include agas phase 101 a, anaqueous phase 101 b′, and anoil phase 101 b″. As one example, themultiphase fluid 101 can include hydrocarbon gas, hydrocarbon liquid, and water (or brine). - The
apparatus 100A includes a U-bend 102 which is configured to flow themultiphase fluid 101. The U-bend 102 includes afirst conduit 102 a, asecond conduit 102 b, and a connectingconduit 102 c. In some implementations, thesecond conduit 102 b is parallel to thefirst conduit 102 a. In some implementations, a longitudinal length of thefirst conduit 102 a is substantially the same as a longitudinal length of thesecond conduit 102 b, and a cross-sectional area of thefirst conduit 102 a is substantially the same as a cross-sectional area of thesecond conduit 102 b, such that a frictional component of the pressure drop experienced by themultiphase fluid 101 flowing through these components (102 a, 102 b) of the U-bend 102 is substantially the same for each component. For example, each of thefirst conduit 102 a and thesecond conduit 102 b have substantially the same inner diameter, d. The connectingconduit 102 c connects thefirst conduit 102 a to thesecond conduit 102 b. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102. In some implementations, the connectingconduit 102 c is perpendicular to thefirst conduit 102 a and to thesecond conduit 102 b. Themultiphase fluid 101 flowing through the U-bend 102 flows into thefirst conduit 102 a, through the connectingconduit 102 c, and out of thesecond conduit 102 b. In some implementations, each of thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c are made of the same material, such that the friction experienced by themultiphase fluid 101 flowing through each of thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c is substantially the same. In some implementations, the connectingconduit 102 b is connected to thefirst conduit 102 a by a firstcurved bend 103 a. In some implementations, the connectingconduit 102 c is connected to thesecond conduit 102 b by a secondcurved bend 103 b. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, the connectingconduit 102 c, the firstcurved bend 103 a, and the secondcurved bend 103 b are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102. The firstcurved bend 103 a and the secondcurved bend 103 b can be made of the same material as thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c, such that the friction experienced by themultiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same. - The
apparatus 100A includes a first pair ofpressure sensors pressure sensors first conduit 102 a viapressure ports pressure sensors multiphase fluid 101 flowing through the U-bend 102. Thepressure ports pressure sensors apparatus 100A includes a second pair ofpressure sensors pressure sensors second conduit 102 b viapressure ports pressure sensors multiphase fluid 101 flowing through the U-bend 102. Thepressure ports pressure sensors pressure ports pressure sensors pressure ports pressure sensors multiphase fluid 101 flowing through thefirst conduit 102 a (measured bypressure sensors second conduit 102 b (measured by thepressure sensors pressure sensors first conduit 102 a via thepressure ports pressure sensors second conduit 102 b via thepressure ports - As shown in
FIG. 1A , the U-bend 102 can be connected to aflow pipe 150 that flows themultiphase fluid 101. Theflow pipe 150 includes afirst pipe 150 a and asecond pipe 150 b. The terms “pipe” and “conduit” are synonymous. The term “pipe” is being used in relation to theflow pipe 150 and the term “conduit” is being used in relation to the U-bend 102 simply for consistency/clarity and to avoid confusion. In some implementations, the U-bend 102 is connected to theflow pipe 150 byangled bends first conduit 102 a of the U-bend 102 is connected to thefirst pipe 150 a of theflow pipe 150 by the firstangled bend 153 a. For example, thesecond conduit 102 b of the U-bend 102 is connected to thesecond pipe 150 b of theflow pipe 150 by the secondangled bend 153 b. In some implementations, as shown inFIG. 1A , the angled bends 153 a, 153 b are 90-degree angled bends. Although shown as 90-degree angled bends inFIG. 1A , the angled bends 153 a, 153 b can have a different degree angle, such as in a range of from 30 degrees to 150 degrees. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, the connectingconduit 102 c, the firstcurved bend 103 a, the secondcurved bend 103 b, the firstangled bend 153 a, the secondangled bend 153 b, and theflow pipe 150 are integrated, such that the U-bend 102 and theflow pipe 150 form a singular, unitary body, as opposed to parts that are disjointed and coupled together. In some implementations, the angled bends 153 a, 153 b are replaced by curved bends (similar to thecurved bends - In some implementations, the inner diameters (d) of the
first conduit 102 a and thesecond conduit 102 b are different from the inner diameter (D) of theflow pipe 150. A change in cross-sectional flow area between theflow pipe 150 and the U-bend 102 can ensure that the differential pressures of themultiphase fluid 101 flowing across the angled bends 153 a, 153 b are predominantly functions of the total flow rate of themultiphase fluid 101 as opposed to other factors, such as frictional pressure losses. In some implementations, the inner diameters (d) of thefirst conduit 102 a and thesecond conduit 102 b can be in a range of from half of the inner diameter (D) of theflow pipe 150 to double the inner diameter (2D) of the flow pipe 150 (that is, D/2≤d≤2D). - In some implementations, each of the pressure sensors (104 a, 104 b, 104 c, 104 d) are at least a threshold distance away from the closest bend. The threshold distance is long enough to allow the flow of the
multiphase fluid 101 to fully develop after the disturbance in flow caused by an upstream bend or long enough to allow the flow of themultiphase fluid 101 to remain fully developed before approaching a downstream bend. Without being bound to theory, the method of sensing (for example, the application and/or objective of the measurement) can determine the location at which the sensors should be placed. For the apparatuses and methods described here, the threshold distance can be, for example, four times the inner diameter, d (that is, 4d). For example, if the inner diameter (d) of the U-bend 102 is 1 inch, the threshold distance is 4 inches. For example, thepressure port 105 a, to which thepressure sensor 104 a is coupled, is located on thefirst conduit 102 a at least 4d distance away from theangled bend 153 a. For example, thepressure port 105 b, to which thepressure sensor 104 b is coupled, is located on thefirst conduit 102 a at least 4d distance away from thecurved bend 103 a. For example, thepressure port 105 c, to which thepressure sensor 104 c is coupled, is located on thesecond conduit 102 b at least 4d distance away from thecurved bend 103 b. For example, thepressure port 105 d, to which thepressure sensor 104 d is coupled, is located on thesecond conduit 102 b at least 4d distance away from theangled bend 153 b. - As shown in
FIG. 1A , theapparatus 100A can be communicatively coupled to acomputer 700. Thecomputer 700 includes aprocessor 705 and amemory 707. Theprocessor 705 can be communicatively coupled to the first pair ofpressure sensors pressure sensors memory 707 is coupled to theprocessor 705. Thecomputer 700 is also shown inFIG. 7 and is described in more detail later. Thememory 707 stores programming instructions for execution by theprocessor 705. The programming instructions can instruct theprocessor 705 to perform various operations. The operations performed by theprocessor 705 can include receiving a first differential pressure signal from the first pair ofpressure sensors multiphase fluid 101 measured by the first pair ofpressure sensors processor 705 can include receiving a second differential pressure signal from the second pair ofpressure sensors multiphase fluid 101 measured by thepressure sensors processor 705 can include determining an overall density of themultiphase fluid 101 at least based on a difference between the first differential pressure and the second differential pressure of themultiphase fluid 101 and the specified differential pressure height, h. - In cases in which the
first conduit 102 a and thesecond conduit 102 b are in a vertical orientation (relative to a reference horizontal, such as ground level), the differential pressure loss ofmultiphase fluid 101 flowing across a vertical distance can be estimated by Equation 1: -
ΔP=ρ×g×h v −ΔP f (1) - where ΔP is the total differential pressure loss of the
multiphase fluid 101, ρ is the apparent mixture density of themultiphase fluid 101, g is acceleration due to gravity, hv is the difference in vertical height of two reference points (such as the locations of thepressure ports pressure ports pressure sensors pressure sensors -
ΔP 1 =ρ×g×h 1 +ΔP f1 (1a) -
ΔP 2 =−ρ×g×h 2 ΔP f2 (1b) - The apparent mixture density of the multiphase fluid (ρ) can be determined by obtaining the difference between the first and second differential pressures (ΔP1−ΔP2) and re-arranging the resulting equation to solve for ρ. The difference between the first and second differential pressures is shown by Equation 2a:
-
ΔP 1 ΔP 2 =ρ×g×h 1 +ΔP f1 +ρ×g×h 2 −ΔP f2 (2a) - Because the flow characteristics of the
first conduit 102 a and thesecond conduit 102 b are substantially the same, ΔPf1 and ΔPf2 can be assumed to be substantially the same (ΔPf1≅ΔPf2), thus Equation 2a can be re-written as Equation 2b: -
ΔP 1 −ΔP 2 =ρ×g×h 1 +ρ×g×h 2 (2b) - In cases in which the first differential pressure (ΔP↑) and the second differential pressure (ΔP↓) are each measured across the same vertical distance, but at opposite flow directions (as is the case for the first pair of
pressure sensors pressure sensors FIG. 1A ), the first vertical height (h1) is equal to the second vertical height (h2)—that is, h1=h2. Thus, Equation 2b can be re-written as Equation 2c: -
ΔP 1 −ΔP 2 =ρ×g×h 1 (2c) - Inputting h as the vertical height for h1 and re-arranging Equation 2c to solve for the overall density of the multiphase fluid (ρ) results in Equation 2d:
-
- The first differential pressure (ΔP1) is measured by the first pair of
pressure sensors pressure sensors multiphase fluid 101. - Additionally, information about the frictional/shear pressure losses can be estimated by adding the first differential pressure (ΔP1) and the second differential pressure (ΔP2), as shown in Equation 2e:
-
ΔP 1 +ΔP 2 =ρ×g×h 1 +ΔP f1 −ρ×g×h 2 +ΔP f2 (2e) - As mentioned previously, in cases where the first vertical height (h1) is equal to the second vertical height (h2), Equation 2e can be re-written as Equation 2f:
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ΔP 1 +ΔP 2 =ΔP f1 +ΔP f2 (2f) - As mentioned previously, because the flow characteristics of the
first conduit 102 a and thesecond conduit 102 b are substantially the same, ΔPf1 and ΔPf2 can be assumed to be substantially the same (ΔPf1≅ΔPf2) and can simply be substituted as ΔPf, thus Equation 2f can be re-written as Equation 2g: -
ΔP1+ΔP 2 =2 x ΔPf (2g) - Re-arranging Equation 2g to solve for frictional/shear pressure losses (ΔPf) provides Equation 2h:
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- The information obtained related to frictional/shear pressure losses (ΔPf) can be useful for determining other correlations and flow characteristics of the
multiphase fluid 101. For example, if theapparatus 100A is used in conjunction with a Venturi-type flowmeter, the information obtained related to frictional/shear pressure losses (ΔPf) can be used to determine correlations of variables used in the Venturi-type flowmeter calculations. For a Venturi-type flowmeter, Bernoulli's equation can be converted into the form shown in Equation 3a: -
m T =C d ×ε×K×√{square root over (2×ρ×(ΔP−k f ×ΔP f))} (3a) - where mT is the total mass flow rate of the
multiphase fluid 101, Cd is the discharge coefficient, ε is the expansion factor, K is a fixed geometry factor (K=A/√{square root over (1−β4)}, where A is the cross-sectional flow area of the Venturi-type flowmeter's neck (d) and β is the beta ratio (d/D, where d is the neck diameter of the Venturi-type flowmeter and D is the upstream pipe which converges with the Venturi-type flowmeter)), ΔP is measured pressure drop including frictional/shear pressure losses, kf is a geometry-based correction factor to account for difference(s) in the shape/geometry of the Venturi-type flowmeter (for example, as inapparatus 100A), ΔPf is frictional/shear pressure losses (for example, measured byapparatus 100A and Equation 2h), and ρ is the mixture density of themultiphase fluid 101. The overall density (ρ) of themultiphase fluid 101 and frictional/shear pressure losses (ΔPf) determined by theapparatus 100A can, for example, be used in conjunction with the information obtained by the Venturi-type flowmeter (for example, total mass flow rate of themultiphase fluid 101, mT) and be input to Equation 3a. - The operations performed by the
processor 705 can include receiving, as input, a gas phase volume fraction (αg) of themultiphase fluid 101. The operations performed by theprocessor 705 can include receiving, as input, a gas phase density (ρg) of thegas phase 101 a themultiphase fluid 101. The operations performed by theprocessor 705 can include receiving, as input, an aqueous phase density (ρa) of theaqueous phase 101 b′ of themultiphase fluid 101. The operations performed by theprocessor 705 can include receiving, as input, an oil phase density (ρo) of theoil phase 101 b″ of themultiphase fluid 101. The operations performed by theprocessor 705 can include determining an aqueous phase volume fraction (αa) of themultiphase fluid 101 at least based on the gas phase volume fraction (αg), the gas density (ρg), the aqueous phase density (ρa), the oil phase density (ρo), and the overall density (ρ) of themultiphase fluid 101. For example, the gas phase volume fraction (αg), the gas density (ρg), the aqueous phase density (ρa), the oil phase density (ρo), and the overall density (ρ) of themultiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the aqueous phase volume fraction (αa) of the multiphase fluid 101: -
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa) (3b) - The operations performed by the
processor 705 can include receiving, as input, an aqueous phase volume fraction (αa) of themultiphase fluid 101. The operations performed by theprocessor 705 can include determining a gas phase volume fraction (αg) of themultiphase fluid 101 at least based on the aqueous phase volume fraction (αa), the gas density (ρg), the aqueous phase density (ρa), the oil phase density (ρo), and the overall density (ρ) of themultiphase fluid 101. For example, the aqueous phase volume fraction (αa), the gas density (ρg), the aqueous phase density (ρa), the oil phase density (ρo), and the overall density (ρ) of themultiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the gas phase volume fraction (αg) of themultiphase fluid 101. - In some implementations, the first pair of
pressure sensors pressure sensors multiphase fluid 101 flowing through the U-bend 102 multiple times across a time duration. Each of the first differential pressures and each of the second differential pressures measured by the first pair ofpressure sensors pressure sensors pressure sensors pressure sensors multiphase fluid 101 taking time to travel from thefirst conduit 102 a (where the first pair ofpressure sensors conduit 102 c, and to thesecond conduit 102 b (where the second pair ofpressure sensors multiphase fluid 101 traveling through the U-bend 102. The time-series data can, for example, be stored in thememory 707. The time-series data can, for example, be used to train and/or build a neural network-based classification model, which can be used to accurately identify flow regimes (for example, bubble flow, mist flow, slug flow, churn flow, annular flow, stratified flow, or intermittent flow). For example, the time-series data can be converted into a spectrogram (for example, by using a Morlet wavelet transform), and a single-layer two-dimensional image can be compiled from the spectrogram. A neural network (machine learning model) can then analyze the image and identify the flow regime of themultiphase fluid 101 flowing through the U-bend 102, for example, based on comparison to historical data. The time-series data can, for example, be used to train and/or build a neural network-based classification model, which can be used to estimate bulk flow velocity of themultiphase fluid 101 flowing through the U-bend 102. For example, the time-series data can be converted into a spectrogram (for example, by using a Morlet wavelet transform), and a single-layer two-dimensional image can be compiled from the spectrogram. A neural network (machine learning model) can then analyze the image and estimate the bulk flow velocity and/or flow rate of themultiphase fluid 101 flowing through the U-bend 102, for example, based on comparison to historical data. -
FIG. 1B depicts anapparatus 100B which can be used to measure a density of amultiphase fluid 101. Theapparatus 100B can be substantially similar to theapparatus 100A shown inFIG. 1A . In comparison, theapparatus 100B omits the connecting conduit (102 c shown inFIG. 1A ). Theapparatus 100B includes the U-bend 102, which includes thefirst conduit 102 a and thesecond conduit 102 b. Thefirst conduit 102 a is connected to thesecond conduit 102 b by acurved bend 103. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, and thecurved bend 103 are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102. Thecurved bend 103 can be made of the same material as thefirst conduit 102 a and thesecond conduit 102 b, such that the friction experienced by themultiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same. - The
apparatus 100B can include a firstdifferential pressure sensor 108 a coupled to thefirst conduit 102 a viapressure ports differential pressure sensor 108 a is configured to measure a first differential pressure of themultiphase fluid 101 flowing through the U-bend 102. Thepressure ports apparatus 100B can include a seconddifferential pressure sensor 108 b coupled to thesecond conduit 102 b viapressure ports differential pressure sensor 108 b is configured to measure a second differential pressure of themultiphase fluid 101 flowing through the U-bend 102. Thepressure ports FIG. 1B , thepressure port 105 a does not necessarily need to be at the same vertical height aspressure port 105 d, and thepressure port 105 b does not necessarily need to be at the same vertical height aspressure port 105 c. Instead, the vertical distance betweenpressure port 105 a andpressure port 105 b should match the vertical distance betweenpressure port 105 c andpressure port 105 d. The height difference between thepressure ports differential pressure sensor 108 a and the height difference between thepressure ports differential pressure sensor 108 b are the same, such that the frictional components of the pressure drops experienced by themultiphase fluid 101 flowing through thefirst conduit 102 a (measured by the firstdifferential pressure sensor 108 a) and through thesecond conduit 102 b (measured by the seconddifferential pressure sensor 108 b) are substantially the same. - Although not shown in
FIG. 1B , theapparatus 100B can be coupled to a flow pipe (such as theflow pipe 150 shown inFIG. 1A ), for example, by angled or curved bends. Although not shown inFIG. 1B , the first and seconddifferential pressure sensors multiphase fluid 101 flowing through the U-bend 102 (for example, usingEquations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, or any combination of these). -
FIG. 1C depicts anapparatus 100C which can be used to measure a density of amultiphase fluid 101. Theapparatus 100C can be substantially similar to theapparatus 100A shown inFIG. 1A . In comparison, theapparatus 100C includes multiple pairs of pressure sensors coupled to thefirst conduit 102 a and multiple pairs of pressure sensors coupled to thesecond conduit 102 b. Theapparatus 100C shown inFIG. 1C includes two pairs of pressure sensors (104 a, 104 b and 104 a′, 104 b′) coupled to thefirst conduit 102 a installed in a parallel configuration, but can, in other embodiments, include additional pairs of pressure sensors. Theapparatus 100C shown inFIG. 1C includes two pairs of pressure sensors (104 c, 104 d and 104 c′, 104 d′) coupled to thesecond conduit 102 b installed in a parallel configuration, but can, in other embodiments, include additional pairs of pressure sensors. The redundancy in pressure sensors can be useful in providing more accurate pressure measurements (for example, by averaging the measured pressures). The redundancy in pressure sensors can also be useful in identifying malfunctions in one or more of the pressure sensors, for example, if one or more of the pressure sensors provide pressure readings that deviate from the remaining pressure sensors by more than a threshold deviation. In some implementations, each pair of pressure sensors can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors pressure sensors 104 a′, 104 b′ can be replaced by a second differential pressure sensor, the pair ofpressure sensors pressure sensors 104 c′, 104 d′ can be replaced by a fourth differential pressure sensor. The redundancy in differential pressure sensors can be useful in providing a wider range of measurements (for example, by using sensors with different, but overlapping ranges). -
FIG. 1D depicts anapparatus 100D which can be used to measure a density of amultiphase fluid 101. Theapparatus 100D can be substantially similar to theapparatus 100A shown inFIG. 1A . In comparison, theapparatus 100D includes more than two pressure sensors coupled to thefirst conduit 102 a and more than two pressure sensors coupled to thesecond conduit 102 b. Although shown inFIG. 1D as including six pressure sensors (104 a, 104 b, 104 c, 104 d, 104 e, 104 f) coupled to thefirst conduit 102 a, theapparatus 100D can include fewer pressure sensors (such as three, four, or five) or more pressure sensors (such as seven or more than seven) coupled to thesecond conduit 102 b. Although shown inFIG. 1D as including six pressure sensors (104 a′, 104 b′, 104 c′, 104 d′, 104 e′, 104 f) coupled to thesecond conduit 102 b, theapparatus 100D can include fewer pressure sensors (such as three, four, or five) or more pressure sensors (such as seven or more than seven) coupled to thesecond conduit 102 b. Ideally, theapparatus 100D would include the same number of pressure sensors coupled to thefirst conduit 102 a as coupled to thesecond conduit 102 b. As shown inFIG. 1D , the pressure sensors (104 a, 104 b, 104 c, 104 d, 104 e, 104 f) are installed on thefirst conduit 102 a in a series configuration, and the pressure sensors (104 a′, 104 b′, 104 c′, 104 d′, 104 e′, 104 f′) are installed on thesecond conduit 102 b in a series configuration. - In some cases, the
pressure sensors first conduit 102 a, corresponding to thepressure sensors 104 a′ and 104 b′ as a corresponding first pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 b′ and 104 c′ as a corresponding second pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 c′ and 104 d′ as a corresponding third pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 d′ and 104 e′ as a corresponding fourth pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 e′ and 104 f′ as a corresponding fifth pair for thesecond conduit 102 b. These pairs can be used to measure a piecewise pressure gradient along the first andsecond conduits multiphase fluid 101 flowing through the U-bend. - In some cases, the
pressure sensors first conduit 102 a, corresponding to thepressure sensors 104 a′ and 104 c′ as a corresponding first pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 b′ and 104 d′ as a corresponding second pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 c′ and 104 e′ as a corresponding third pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 d′ and 104 f′ as a corresponding fourth pair for thesecond conduit 102 b. Similarly, these pairs can be used to measure a piecewise pressure gradient along the first andsecond conduits multiphase fluid 101 flowing through the U-bend. - In some cases, the
pressure sensors first conduit 102 a, corresponding to thepressure sensors 104 a′ and 104 d′ as a corresponding first pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 b′ and 104 e′ as a corresponding second pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 c′ and 104 f′ as a corresponding third pair for thesecond conduit 102 b. Similarly, these pairs can be used to measure a piecewise pressure gradient along the first andsecond conduits multiphase fluid 101 flowing through the U-bend. - In some cases, the
pressure sensors first conduit 102 a, corresponding to thepressure sensors 104 a′ and 104 e′ as a corresponding first pair for thesecond conduit 102 b. In some cases, thepressure sensors first conduit 102 a, corresponding to thepressure sensors 104 b′ and 104 f′ as a corresponding second pair for thesecond conduit 102 b. Similarly, these pairs can be used to measure a piecewise pressure gradient along the first andsecond conduits multiphase fluid 101 flowing through the U-bend. - In some cases, the
pressure sensors first conduit 102 a, corresponding to thepressure sensors 104 a′ and 104 f′ as a corresponding first pair for thesecond conduit 102 b. In such cases, theapparatus 100D is substantially the same as theapparatus 100A shown inFIG. 1A . Any combinations or sub-combinations of the aforementioned pairs or pressure sensors can be considered as suitable implementations of theapparatus 100D. - In some implementations, any pair of pressure sensors coupled to the first tubular 102 a can be replaced by a differential pressure sensor. For example, the pair of
pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors pressure sensors - In some implementations, any pair of pressure sensors coupled to the second tubular 102 b can be replaced by a differential pressure sensor. For example, the pair of
pressure sensors 104 a′, 104 b′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 a′, 104 c′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 a′, 104 d′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 a′, 104 e′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 a′, 104 f′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 b′, 104 c′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 b′, 104 d′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 b′, 104 e′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 b′, 104 f′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 c′, 104 d′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 c′, 104 e′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 c′, 104 f′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 d′, 104 e′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 d′, 104 f′ can be replaced by a differential pressure sensor. For example, the pair ofpressure sensors 104 e′, 104 f′ can be replaced by a differential pressure sensor. -
FIG. 1E depicts anapparatus 100E which can be used to measure a total mass flow rate of amultiphase fluid 101. Theapparatus 100E can be substantially similar to theapparatus 100A shown inFIG. 1A . The first pair ofpressure sensors pressure sensors apparatus 100E in comparison to theapparatus 100A. Thefirst pressure sensor 104 a is coupled to thepressure port 105 a on thefirst pipe 150 a (third conduit) of theflow pipe 150. Thesecond pressure sensor 104 b is coupled to thepressure port 105 b on thefirst conduit 102 a of the U-bend 102. Thethird pressure sensor 104 c is coupled to thepressure port 105 c on thesecond conduit 102 b of the U-bend 102. Thefourth pressure sensor 104 d is coupled topressure port 105 d on the thesecond pipe 150 b (fourth conduit) of theflow pipe 150. In some implementations, the first pair ofpressure sensors pressure sensors - The first pair of
pressure sensors multiphase fluid 101. The first differential pressure includes the pressure losses of themultiphase fluid 101 flowing through the firstangled bend 153 a. The second pair ofpressure sensors multiphase fluid 101. The second differential pressure includes the pressure losses of themultiphase fluid 101 flowing through the secondangled bend 153 b. The operations performed by theprocessor 705 can include receiving a first differential pressure signal from the first pair ofpressure sensors multiphase fluid 101 measured by thepressure sensors processor 705 can include receiving a second differential pressure signal from the second pair ofpressure sensors multiphase fluid 101 measured by thepressure sensors processor 705 can include determining an overall flow rate of themultiphase fluid 101 at least based on the first differential pressure, the second differential pressure, a difference between the first differential pressure and the second differential pressure of themultiphase fluid 101 and the overall density of themultiphase fluid 101. The overall density of themultiphase fluid 101 can be measured, for example, by a separate multiphase flowmeter. For example, theapparatus 100E can include features from theapparatus 100A, which can be used to determine the mixture density (ρ) of themultiphase fluid 101. - The overall flow rate of the
multiphase fluid 101 can be determined in various ways. As a first example, the overall flow rate of the multiphase fluid 101 (ignoring frictional pressure loss) can be determined using the first differential pressure by Equation 4a: -
m T1 C d1 ×ε 1 ×K 1×√{square root over (2×ρ×(ΔP 1 −ρ×g×h v))} (4a) - where mT1 is the total mass flow rate of the
multiphase fluid 101, Cd1 is an empirically characterized discharge coefficient, ε1 is an expansion factor, K1 is a fixed geometry factor (K1=A1/√{square root over (1−β1 4)}, where A1 is the cross-sectional flow area of the throat of the firstangled bend 153 a and β1 is the beta ratio (d/D, where d is the inner diameter of thefirst conduit 102 a and D is the inner diameter of thefirst pipe 150 a)), ΔP1 is the first differential pressure measured by thepressure sensors multiphase fluid 101, g is the acceleration due to gravity, and hv is the vertical height difference between thepressure ports pressure sensors - As a second example, the total mass flow rate of the multiphase fluid 101 (ignoring frictional pressure loss) can be determined using the second differential pressure by Equation 4b:
-
m T2 C d2 ×ε 2 ×K 2×√{square root over (2×ρ×(ΔP 2 −ρ×g×h v))} (4b) - where mT2 is the total mass flow rate of the
multiphase fluid 101, Cd2 is an empirically characterized discharge coefficient, ε2 is an expansion factor, K2 is a fixed geometry factor (K2=A2/√{square root over (1−β2 4)}, where A2 is the cross-sectional flow area of the throat of the secondangled bend 153 b and β2 is the beta ratio (D/d, where d is the inner diameter of thesecond conduit 102 b and D is the inner diameter of thesecond pipe 150 b)), ΔP2 is the second differential pressure measured by thepressure sensors multiphase fluid 101, g is the acceleration due to gravity, and hv is the vertical height difference between thepressure ports pressure sensors - The operations performed by the
processor 705 can include comparing the total mass flow rates (mT1, mT2) determined by Equations 4a and 4b to determine an adjustment of the discharge coefficients (Cd1, Cd2). Equation 4a can be re-written as: mT1=Cd1×Y1, where Y1 simply substitutes the right-hand side of Equation 4a (including measured parameters ΔP1 and ρ and predetermined parameters ε1 and K1) excluding the discharge coefficient Cd1. Equation 4b can be re-written as: mT2=Cd2×Y2, where Y2 simply substitutes the right-hand side of Equation 4b (including measured parameters ΔP2 and ρ and predetermined parameters ε2 and K2) excluding the discharge coefficient Cd1. Because the total mass flow rate does not change as themultiphase fluid 101 flows through theapparatus 100E, mT1=mT2. Thus, Cd1×Y1=Cd2×Y2. Because of this relationship, given Cd1 and the measured parameters Y1 and Y2, Cd2 can be calculated. Similarly, given Cd2 and the measured parameters Y1 and Y2, Cd1 can be calculated. As such, the discharge coefficients (Cd1, Cd2) can be verified for consistency and accuracy, as an in situ self-check. Other techniques (such as least-squares minimization) can be additionally or alternatively used to accurately calculate the discharge coefficients (Cd1, Cd2). - The first differential pressure (ΔP1) measured by the
pressure sensors pressure sensors multiphase fluid 101. Equation 4a can be re-arranged as Equation 5a: -
- Equation 4b can be re-arranged as Equation 5b:
-
- As mentioned previously, the total mass flow rate does not change as the
multiphase fluid 101 flows through theapparatus 100E, so mT1=mT2. For simplicity, the variable Z is defined by Equation 5c: -
- Combining Equations 5a, 5b, and 5c and then solving for the mixture density (ρ) results in Equation 5d:
-
- Equation 5d can be used, for example, to verify the accuracy of the mixture density (ρ) determined by any one of
apparatuses - In some implementations, a distance between the
first pressure sensor 104 a and thesecond pressure sensor 104 b is substantially the same as a distance between thethird pressure sensor 104 c and thefourth pressure sensor 104 d. In a specific example, theapparatus 100E has the following dimensions. The inner diameter (d) of the U-bend 102 (thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c) is about 2.067 inches (nominal pipe size (NPS) 2″ Schedule 40). The inner diameter (D) of thefirst pipe 150 a and thesecond pipe 150 b is about 3.068″ (NPS 3″ Schedule 40). The dimension A is the length of straight pipe (that is, pipe that is free of any bends) of thefirst pipe 150 a upstream of thefirst pressure sensor 104 a. The dimension A is also the length of straight pipe of thesecond pipe 150 b downstream of thefourth pressure sensor 104 d. The dimension A is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair ofpressure sensors pressure sensors first pipe 150 a (A≥5D). The dimension B is the length of straight pipe of thefirst pipe 150 a downstream of thefirst pressure sensor 104 a and upstream of the firstangled bend 153 a. The dimension B is also the length of straight pipe of thesecond pipe 150 b downstream of the secondangled bend 153 b and upstream of thefourth pressure sensor 104 d. Similarly, the dimension B is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair ofpressure sensors pressure sensors first pipe 150 a (B≥5D). The dimension C is the length of straight pipe of thefirst conduit 102 a downstream of the firstangled bend 153 a and upstream of thesecond pressure sensor 104 b. The dimension C is also the length of straight pipe of thesecond conduit 102 b downstream of thethird pressure sensor 104 c and upstream of the secondangled bend 153 b. Similarly, the dimension C is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair ofpressure sensors pressure sensors -
FIG. 1F depicts anapparatus 100F which can be used to measure a total mass flow rate of amultiphase fluid 101. Theapparatus 100F can be substantially similar to theapparatus 100E shown inFIG. 1E . In comparison, theapparatus 100F omits the connecting conduit (102 c shown inFIG. 1E ). Theapparatus 100F includes the U-bend 102, which includes thefirst conduit 102 a and thesecond conduit 102 b. Thefirst conduit 102 a is connected to thesecond conduit 102 b by acurved bend 103. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, and thecurved bend 103 are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102. Thecurved bend 103 can be made of the same material as thefirst conduit 102 a and thesecond conduit 102 b, such that the friction experienced by themultiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same. - As shown in
FIG. 1F , the U-bend 102 can be connected to aflow pipe 150 that flows themultiphase fluid 101. Theflow pipe 150 includes thefirst pipe 150 a and thesecond pipe 150 b. In some implementations, the U-bend 102 is connected to theflow pipe 150 by curved bends 153 c, 153 d. For example, thefirst conduit 102 a of the U-bend 102 is connected to thefirst pipe 150 a of theflow pipe 150 by the first curved bend 153 c. For example, thesecond conduit 102 b of the U-bend 102 is connected to thesecond pipe 150 b of theflow pipe 150 by the second curved bend 153 d. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, thecurved bend 103, the first curved bend 153 c, the second curved bend 153 d, and theflow pipe 150 are integrated, such that the U-bend 102 and theflow pipe 150 form a singular, unitary body, as opposed to parts that are disjointed and coupled together. - The
apparatus 100F can include a firstdifferential pressure sensor 108 a coupled to thefirst pipe 150 a and to thefirst conduit 102 a viapressure ports differential pressure sensor 108 a is configured to measure a first differential pressure of themultiphase fluid 101 flowing across the first curved bend 153 c. Thepressure ports apparatus 100B can include a seconddifferential pressure sensor 108 b coupled to thesecond conduit 102 b and to thesecond pipe 150 b viapressure ports differential pressure sensor 108 b is configured to measure a second differential pressure of themultiphase fluid 101 flowing across the second curved bend 153 d. Thepressure ports FIG. 1F , thepressure port 105 a does not necessarily need to be at the same vertical height aspressure port 105 d, and thepressure port 105 b does not necessarily need to be at the same vertical height aspressure port 105 c. Instead, the vertical distance betweenpressure port 105 a andpressure port 105 b should match the vertical distance betweenpressure port 105 c andpressure port 105 d. The height difference between thepressure ports differential pressure sensor 108 a and the height difference between thepressure ports differential pressure sensor 108 b are the same, and the horizontal distance between thepressure ports differential pressure sensor 108 a and the horizontal distance between thepressure ports differential pressure sensor 108 b are the same, such that the frictional components of the pressure drops experienced by themultiphase fluid 101 flowing across the first curved bend 153 c (measured by the firstdifferential pressure sensor 108 a) and through the second curved bend 153 d (measured by the seconddifferential pressure sensor 108 b) are substantially the same. - Although not shown in
FIG. 1F , the first and seconddifferential pressure sensors multiphase fluid 101 flowing through the U-bend 102 (for example, using Equations 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these). -
FIG. 1G depicts anapparatus 100G which can be used to measure a water-liquid ratio of amultiphase fluid 101. Theapparatus 100G can be substantially similar to theapparatus 100A shown inFIG. 1A . In comparison to theapparatus 100A, theapparatus 100G includesdynamic pressure sensors FIG. 1G as including threedynamic pressure sensors apparatus 100G can include fewer dynamic pressure sensors (such as two dynamic pressure sensors) or more dynamic pressure sensors (such as four dynamic pressure sensors or more than four dynamic pressure sensors). Thedynamic pressure sensors multiphase fluid 101 flowing through the U-bend 102, as opposed to a static pressure of themultiphase fluid 101. Thedynamic pressure sensors dynamic pressure sensors first conduit 102 a of the U-bend 102. In some implementations, thedynamic pressure sensors second conduit 102 b of the U-bend 102. In some implementations, a first portion of thedynamic pressure sensors dynamic pressure sensors first conduit 102 a of the U-bend 102, and a remaining portion of thedynamic pressure sensors second conduit 102 b of the U-bend 102. Thedynamic pressure sensors - The dynamic pressure measurements taken by the
dynamic pressure sensors multiphase fluid 101 flowing through the U-bend 102. The speed of sound of themultiphase fluid 101 and the overall density (ρ) of themultiphase fluid 101 can then be used to determine the water-liquid ratio of themultiphase fluid 101. The water-liquid ratio of themultiphase fluid 101 is a ratio of a volume of theaqueous phase 101 b′ to a sum of the volume of theaqueous phase 101 b′ and a volume of theoil phase 101 b″ (liquid phase 101 b) (that is, the ratio of (volume of 101 b′)/(volume of 101 b′+volume of 101 b″), which is the same as the ratio of (volume of 101 b′)/(volume of 101 b)). For example, the speed of sound of themultiphase fluid 101 and the overall density (ρ) of themultiphase fluid 101 can be compared to a plotted graph of various phase curves (gas/oil, gas/aqueous, oil/aqueous) to determine the water-liquid ratio. -
FIG. 1H depicts anapparatus 100H which can be used to measure a density, a total flow rate, and phase flow rates of amultiphase fluid 101. Theapparatus 100H can be substantially similar to theapparatus 100A shown inFIG. 1A and theapparatus 100E shown inFIG. 1E . For example, theapparatus 100H can be a combination of theapparatus 100A and theapparatus 100E. Thefirst pressure sensor 104 a is coupled to afirst pressure port 105 a on thefirst pipe 150 a (third conduit) of theflow pipe 150. Thesecond pressure sensor 104 b is coupled to asecond pressure port 105 b on thefirst conduit 102 a of the U-bend 102. Thethird pressure sensor 104 c is coupled to athird pressure port 105 c on thesecond conduit 102 b of the U-bend 102. Thefourth pressure sensor 104 d is coupled to afourth pressure port 105 d on thesecond pipe 150 b (fourth conduit) of theflow pipe 150. The fifth andsixth pressure sensors sixth pressure ports first conduit 102 a of the U-bend 102. The fifth andsixth pressure ports first conduit 102 a. The seventh andeighth pressure sensors 104 g, 104 h are coupled to seventh andeighth pressure ports second conduit 102 b of the U-bend 102. The seventh andeighth pressure ports second conduit 102 b. In some implementations, the first andsecond pressure sensors fourth pressure sensors sixth pressure sensors eighth pressure sensors 104 g, 104 h are replaced by a fourth differential pressure sensor. - The first pair of
pressure sensors multiphase fluid 101. The first differential pressure includes the pressure losses of themultiphase fluid 101 flowing through the firstangled bend 153 a. The second pair ofpressure sensors multiphase fluid 101. The second differential pressure includes the pressure losses of themultiphase fluid 101 flowing through the secondangled bend 153 b. The third pair ofpressure sensors multiphase fluid 101. The fourth pair ofpressure sensors 104 g, 104 h (or fourth differential pressure sensor) are configured to measure a fourth differential pressure of themultiphase fluid 101. The operations performed by theprocessor 705 can include receiving a first differential pressure signal from the first pair ofpressure sensors multiphase fluid 101 measured by thepressure sensors processor 705 can include receiving a second differential pressure signal from the second pair ofpressure sensors multiphase fluid 101 measured by thepressure sensors processor 705 can include receiving a third differential pressure signal from the third pair ofpressure sensors multiphase fluid 101 measured by thepressure sensors processor 705 can include receiving a fourth differential pressure signal from the fourth pair ofpressure sensors 104 g, 104 h (or fourth differential pressure sensor). The fourth differential pressure signal can represent the fourth differential pressure of themultiphase fluid 101 measured by thepressure sensors 104 g, 104 h (or fourth differential pressure sensor). The operations performed by theprocessor 705 can include determining an overall density of themultiphase fluid 101 at least based on the specified height (h) and a difference between the third differential pressure and the fourth differential pressure. The operations performed by theprocessor 705 can include determining an overall flow rate of themultiphase fluid 101 at least based on the first differential pressure and the second differential pressure of themultiphase fluid 101 and the overall density of themultiphase fluid 101. - The mixture density of the
multiphase fluid 101 can be determined in various ways. As a first example, the mixture density (ρ) of themultiphase fluid 101 can be determined by Equation 2d tailored for theapparatus 100H, where ΔP1 is the third differential pressure measured by the third pair ofpressure sensors pressure sensors 104 g, 104 h (or fourth differential pressure sensor), and h2 is the specified height (h). As a second example, the mixture density (ρ) of themultiphase fluid 101 can be determined by Equation 5d tailored for theapparatus 100H, where ΔP1 is the third differential pressure measured by the third pair ofpressure sensors pressure sensors 104 g, 104 h (or fourth differential pressure sensor). - The total flow rate of the
multiphase fluid 101 can be determined in various ways. As a first example, the total flow rate of themultiphase fluid 101 can be determined using the first differential pressure by Equation 4a. As a second example, the total flow rate of themultiphase fluid 101 can be determined using the second differential pressure by Equation 4b. The operations performed by theprocessor 705 can include comparing the overall flow rates (mT1, mT2) determined by Equations 4a and 4bc to determine an adjustment of the discharge coefficients (Cd1, Cd2). - In some implementations, a distance between the
first pressure sensor 104 a and thesecond pressure sensor 104 b is substantially the same as a distance between thethird pressure sensor 104 c and thefourth pressure sensor 104 d. In a specific example, theapparatus 100D has the following dimensions. The inner diameter (d) of the U-bend 102 (thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c) is about 2.067 inches (NPS 2″ Schedule 40). The inner diameter (D) of thefirst pipe 150 a and thesecond pipe 150 b is about 3.068″ (NPS 3″ Schedule 40). The dimension A is the length of straight pipe (that is, pipe that is free of any bends) of thefirst pipe 150 a upstream of thefirst pressure sensor 104 a. The dimension A is also the length of straight pipe of thesecond pipe 150 b downstream of thefourth pressure sensor 104 d. The dimension A is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair ofpressure sensors pressure sensors first pipe 150 a (A≥5D). The dimension B is the length of straight pipe of thefirst pipe 150 a downstream of thefirst pressure sensor 104 a and upstream of the firstangled bend 153 a. The dimension B is also the length of straight pipe of thesecond pipe 150 b downstream of the secondangled bend 153 b and upstream of thefourth pressure sensor 104 d. Similarly, the dimension B is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair ofpressure sensors pressure sensors first pipe 150 a (B≥5D). The dimension C is the length of straight pipe of thefirst conduit 102 a downstream of the firstangled bend 153 a and upstream of thesecond pressure sensor 104 b. The dimension C is also the length of straight pipe of thesecond conduit 102 b downstream of thethird pressure sensor 104 c and upstream of the secondangled bend 153 b. Similarly, the dimension C is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the first pair ofpressure sensors pressure sensors second pressure sensor 104 b and thefifth pressure sensor 104 e of at least two times the inner diameter (d) of the U-bend 102 (≥2d) along the longitudinal length of thefirst conduit 102 a of the U-bend 102. In some implementations, there is a length of straight pipe between theeighth pressure sensor 104 h and thethird pressure sensor 104 c of at least two times the inner diameter (d) of the U-bend 102 (≥2d) along the longitudinal length of thesecond conduit 102 b of the U-bend 102. The dimension E is the length of straight pipe of thefirst conduit 102 a downstream of thesixth pressure sensor 104 f and upstream of the firstcurved bend 103 a. The dimension E is also the length of straight pipe of thesecond conduit 102 b downstream of the secondcurved bend 103 b and upstream of the seventh pressure sensor 104 g. Similarly, the dimension E is a minimum length of straight pipe that ensures minimal interference of turbulence and friction which may affect the measurements taken by the third pair ofpressure sensors pressure sensors 104 g, 104 h. In some implementations, the dimension E is at least five times the inner diameter (d) of the U-bend 102 (E≥5d). -
FIG. 1I depicts an apparatus 100I which can be used to measure a density, a flow rate, and a water-liquid ratio of amultiphase fluid 101. The apparatus 100I can be substantially similar to theapparatus 100A shown inFIG. 1A , theapparatus 100E shown inFIG. 1E , theapparatus 100G shown inFIG. 1G , and theapparatus 100H shown inFIG. 1H . For example, the apparatus 100I can be a combination of theapparatus 100G and theapparatus 100H. For example, the apparatus 100I can be a copy of theapparatus 100H that also includesdynamic pressure sensors apparatus 100G) that are coupled to the U-bend 102. Thus, the apparatus 100I can perform all of the functions that can be performed by theapparatus 100G and also by theapparatus 100H. - Although shown in
FIG. 1I as including threedynamic pressure sensors dynamic pressure sensors multiphase fluid 101 flowing through the U-bend 102, as opposed to a static pressure of themultiphase fluid 101. Thedynamic pressure sensors dynamic pressure sensors first conduit 102 a of the U-bend 102. In some implementations, thedynamic pressure sensors second conduit 102 b of the U-bend 102. In some implementations, a first portion of thedynamic pressure sensors dynamic pressure sensors first conduit 102 a of the U-bend 102, and a remaining portion of thedynamic pressure sensors second conduit 102 b of the U-bend 102. Thedynamic pressure sensors - The dynamic pressure measurements taken by the
dynamic pressure sensors multiphase fluid 101 flowing through the U-bend 102. The speed of sound of themultiphase fluid 101 and the overall density (ρ) of themultiphase fluid 101 can then be used to determine the water-liquid ratio of themultiphase fluid 101. For example, the speed of sound of themultiphase fluid 101 and the overall density (ρ) of themultiphase fluid 101 can be compared to a plotted graph of various phase curves (gas/oil, gas/aqueous, oil/aqueous) to determine the water-liquid ratio. -
FIG. 1J depicts anapparatus 100J which can be used to measure a density, a flow rate, and a water-liquid ratio of amultiphase fluid 101. Theapparatus 100J can be substantially similar to theapparatus 100H shown inFIG. 1H . In comparison, theapparatus 100J omits the connecting conduit (102 c shown inFIG. 1H ). Theapparatus 100J includes the U-bend 102, which includes thefirst conduit 102 a and thesecond conduit 102 b. Thefirst conduit 102 a is connected to thesecond conduit 102 b by acurved bend 103. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, and thecurved bend 103 are integrated, such that the U-bend 102 is a singular, unitary body, as opposed to parts that are disjointed and coupled together to form the U-bend 102. Thecurved bend 103 can be made of the same material as thefirst conduit 102 a and thesecond conduit 102 b, such that the friction experienced by themultiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same. - As shown in
FIG. 1J , the U-bend 102 can be connected to aflow pipe 150 that flows themultiphase fluid 101. Theflow pipe 150 includes thefirst pipe 150 a and thesecond pipe 150 b. In some implementations, the U-bend 102 is connected to theflow pipe 150 by curved bends 153 c, 153 d. For example, thefirst conduit 102 a of the U-bend 102 is connected to thefirst pipe 150 a of theflow pipe 150 by the first curved bend 153 c. For example, thesecond conduit 102 b of the U-bend 102 is connected to thesecond pipe 150 b of theflow pipe 150 by the second curved bend 153 d. In some implementations, thefirst conduit 102 a, thesecond conduit 102 b, thecurved bend 103, the first curved bend 153 c, the second curved bend 153 d, and theflow pipe 150 are integrated, such that the U-bend 102 and theflow pipe 150 form a singular, unitary body, as opposed to parts that are disjointed and coupled together. - The
apparatus 100J can include a firstdifferential pressure sensor 108 a coupled to thefirst pipe 150 a and to thefirst conduit 102 a viapressure ports differential pressure sensor 108 a is configured to measure a first differential pressure of themultiphase fluid 101 flowing across the first curved bend 153 c. Thepressure ports apparatus 100B can include a seconddifferential pressure sensor 108 b coupled to thesecond conduit 102 b and to thesecond pipe 150 b viapressure ports differential pressure sensor 108 b is configured to measure a second differential pressure of themultiphase fluid 101 flowing across the second curved bend 153 d. Thepressure ports FIG. 1F , thepressure port 105 a does not necessarily need to be at the same vertical height aspressure port 105 d, and thepressure port 105 b does not necessarily need to be at the same vertical height aspressure port 105 c. Instead, the vertical distance betweenpressure port 105 a andpressure port 105 b should match the vertical distance betweenpressure port 105 c andpressure port 105 d. The height difference between thepressure ports differential pressure sensor 108 a and the height difference between thepressure ports differential pressure sensor 108 b are the same, and the horizontal distance between thepressure ports differential pressure sensor 108 a and the horizontal distance between thepressure ports differential pressure sensor 108 b are the same, such that the frictional components of the pressure drops experienced by themultiphase fluid 101 flowing across the first curved bend 153 c (measured by the firstdifferential pressure sensor 108 a) and through the second curved bend 153 d (measured by the seconddifferential pressure sensor 108 b) are substantially the same. - The
apparatus 100J can include a thirddifferential pressure sensor 108 c coupled to thefirst conduit 102 a viapressure ports differential pressure sensor 108 c is configured to measure a third differential pressure of themultiphase fluid 101 flowing through the U-bend 102. Thepressure ports apparatus 100J can include a fourthdifferential pressure sensor 108 d coupled to thesecond conduit 102 b viapressure ports differential pressure sensor 108 d is configured to measure a fourth differential pressure of themultiphase fluid 101 flowing through the U-bend 102. Thepressure ports FIG. 1J , thepressure port 105 e does not necessarily need to be at the same vertical height aspressure port 105 h, and thepressure port 105 f does not necessarily need to be at the same vertical height aspressure port 105 g. Instead, the vertical distance betweenpressure port 105 e andpressure port 105 f should match the vertical distance betweenpressure port 105 g andpressure port 105 h. The height difference between thepressure ports differential pressure sensor 108 c and the height difference between thepressure ports differential pressure sensor 108 d are the same, such that the frictional components of the pressure drops experienced by themultiphase fluid 101 flowing through thefirst conduit 102 a (measured by the thirddifferential pressure sensor 108 c) and through thesecond conduit 102 b (measured by the fourthdifferential pressure sensor 108 d) are substantially the same. - Although not shown in
FIG. 1J , the first, second, third, and fourthdifferential pressure sensors multiphase fluid 101 flowing through the U-bend 102 (for example, usingEquations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these). - Any of the
apparatuses -
FIG. 2A is a schematic diagram depicting various example pressure tap arrangements. Each of the views (i), (ii), and (iii) are cross-sectional views of a pipe (for example, thefirst conduit 102 a or thesecond conduit 102 b). Any of the pressure sensors (104 a, 104 b, 104 c, 104 d, 104 e, 104 f, 104 a′, 104 b′, 104 c′, 104 d′, 104 e′, 104 f′) can have the form shown in view (i), (ii), or (iii). In view (i), the pressure sensor includes a single pressure tap. In view (ii), the pressure sensor includes various pressure taps (for example, four) that are distributed around a circumference of the conduit. In view (ii), the pressure sensor can obtain four simultaneous readings (one at each of the four pressure taps) and average the four simultaneous readings to obtain an averaged pressure reading for that particular axial location along the conduit. Although shown in view (ii) as having four pressure taps, the pressure sensors can have fewer pressure taps (such as two or three) or more pressure taps (such as five or more than five). In view (iii), the pressure sensor includes a circumferential pressure tap that fully spans the entire circumference of the conduit. The circumferential pressure tap shown in view (iii) may be the most accurate out of all the views (i), (ii), and (iii) shown inFIG. 2A . -
FIG. 2B is a schematic diagram depicting various example piping arrangements. Each of the views (i), (ii), (iii), (iv), and (v) depict piping arrangements that can used in addition to or alternatively to the piping arrangements already described with respect to theapparatuses multiphase fluid 101 flowing through the respective piping arrangement. ΔP2 is a second differential pressure of themultiphase fluid 101 flowing through the respective piping arrangement. ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first and second differential pressures (ΔP1, ΔP2) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of themultiphase fluid 101 flowing through the respective piping arrangement (for example, usingEquations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, or any combination of these). - As an example, view (i) can be considered a base case that generally conforms to the piping arrangements of
apparatuses FIGS. 1A and 1B , respectively. The piping arrangement of view (ii) is substantially similar to the piping arrangement of view (i), but the first andsecond conduits second conduits multiphase fluid 101 flowing through the piping arrangement of view (iv) flows downward before flowing upward. The piping arrangement of view (v) is substantially similar to the piping arrangement of view (i), but the first andsecond conduits -
FIG. 2C is a schematic diagram depicting various example piping arrangements. Each of the views (i), (ii), (iii), (iv), and (v) depict piping arrangements that can used in addition to or alternatively to the piping arrangements already described with respect to theapparatuses multiphase fluid 101 flowing through the respective piping arrangement across a first bend (curved or angled). ΔP2 is a second differential pressure of themultiphase fluid 101 flowing through the respective piping arrangement across a second bend (curved or angled). ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first and second differential pressures (ΔP1, ΔP2) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, or both) of themultiphase fluid 101 flowing through the respective piping arrangement (for example, using Equations 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these). - As an example, view (i) can be considered a base case that generally conforms to the piping arrangements of
apparatuses FIGS. 1E and 1F , respectively. The piping arrangement of view (ii) is substantially similar to the piping arrangement of view (i), but the first andsecond conduits second conduits multiphase fluid 101 flowing through the piping arrangement of view (iv) flows downward before flowing upward. The piping arrangement of view (v) is substantially similar to the piping arrangement of view (i), but the first andsecond conduits -
FIG. 2D is a schematic diagram depicting various example piping arrangements. Each of the views (i), (ii), (iii), and (iv) depict piping arrangements that can used in addition to or alternatively to the piping arrangements already described with respect to theapparatuses multiphase fluid 101 flowing through the respective piping arrangement across a first bend (curved or angled). ΔP2 is a second differential pressure of themultiphase fluid 101 flowing through the respective piping arrangement across a second bend (curved or angled). ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. ΔP3 is a third differential pressure of themultiphase fluid 101 flowing through thefirst conduit 102 a of the respective piping arrangement. ΔP4 is a fourth differential pressure of themultiphase fluid 101 flowing through thesecond conduit 102 b of the respective piping arrangement. ΔP3 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP4 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first, second, third, and fourth differential pressures (ΔP1, ΔP2, ΔP3, ΔP4) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of themultiphase fluid 101 flowing through the respective piping arrangement (for example, usingEquations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these). - As an example, view (i) can be considered a base case that generally conforms to the piping arrangements of
apparatuses FIGS. 1H and 1J , respectively. The piping arrangement of view (ii) is substantially similar to the piping arrangement of view (i), but the first andsecond conduits second pipes flow pipe 150 are not in-line with one another. The piping arrangement of view (iv) is substantially similar to the piping arrangement of view (i), but is flipped vertically, such that themultiphase fluid 101 flowing through the piping arrangement of view (iv) flows downward before flowing upward. -
FIG. 2E is a schematic diagram depicting various example piping arrangements. Each of the views (i), (ii), (iii), and (iv) depict piping arrangements that can used in addition to or alternatively to the piping arrangements already described with respect to theapparatuses multiphase fluid 101 flowing through the respective piping arrangement across a first bend (curved or angled). ΔP2 is a second differential pressure of themultiphase fluid 101 flowing through the respective piping arrangement across a second bend (curved or angled). ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. ΔP3 is a third differential pressure of themultiphase fluid 101 flowing through thefirst conduit 102 a of the respective piping arrangement. ΔP4 is a fourth differential pressure of themultiphase fluid 101 flowing through thesecond conduit 102 b of the respective piping arrangement. ΔP3 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP4 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first, second, third, and fourth differential pressures (ΔP1, ΔP2, ΔP3, ΔP4) measured from any of these piping arrangements can be used, for example, to determine characteristics (such as a mixture density, a total mass flow rate, an aqueous phase volume fraction, a gas phase volume fraction, or any combination of these) of themultiphase fluid 101 flowing through the respective piping arrangement (for example, usingEquations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these). - The piping arrangement of view (i) is substantially similar to the piping arrangements of
apparatuses FIGS. 1H and 1J , respectively, but the first andsecond conduits second conduits FIG. 2D , but the first andsecond conduits second conduits second pipes flow pipe 150 are not in-line with one another -
FIG. 2F is a schematic diagram depicting various example sensor arrangements. Any of the sensor arrangements shown in views (i), (ii), (iii), (iv), and (v) can be applied (either alone or in combination) in addition to or alternatively to the sensor arrangements already described with respect to theapparatuses - As an example, view (i) can be considered a base case that generally conforms to the differential pressure sensor arrangements of
apparatuses FIGS. 1B, 1F, and 1J , respectively. The pressure sensor arrangement of view (ii) includes two pressure sensors which measure static pressure at their respective locations. A difference between the measured static pressures can be determined as a differential pressure (similar to the differential pressure sensor). The pressure sensor arrangement of view (ii) is substantially similar to the pressure sensor arrangements shown in theapparatuses FIGS. 1A, 1C, 1D, 1E, 1G, 1H, and 1I , respectively. The differential pressure sensor arrangement of view (iii) is substantially similar to the view (i) but includes redundant differential pressure sensors in a parallel configuration across the same length of piping, which is substantially similar to the differential pressure sensor arrangement shown inapparatus 100C ofFIG. 1C . The differential pressure sensor arrangement of view (iv) is substantially similar to the differential pressure sensor arrangement of view (i), but includes additional differential pressure sensors in a series configuration across a length of piping, which is substantially similar to the differential pressure sensor arrangement shown inapparatus 100D ofFIG. 1D . The sensor arrangement of view (v) includes multiple strain sensors (such as strain gauges) disposed along a length of piping. The measured strain can be correlated to pressure, such that similar calculations can be completed to determine characteristics of the flowingmultiphase fluid 101. -
FIG. 3A is a flowchart depicting an example multiphasefluid flow model 300A. Any one of theapparatuses model 300A to characterize a multiphase fluid, such as themultiphase fluid 101. At block 301 a, pressure and temperature of themultiphase fluid 101 is determined (for example, using pressure and temperature sensors). At block 303 a, various properties (such as the density, viscosity, and speed of sound) of the phases (gas phase 101 a,aqueous phase 101 b′, andoil phase 101 b″) of themultiphase fluid 101 are determined. For example, the gas phase density (ρg) of thegas phase 101 a, the aqueous phase density (ρa) of theaqueous phase 101 b′, and the oil phase density (ρo) of theoil phase 101 b″ are determined at block 303 a. At block 305 a, a total flow rate (mT) of themultiphase fluid 101 is determined (for example, using differential pressure sensors as in theapparatus 100D). At block 307 a, a mixture density (ρ) of themultiphase fluid 101 is determined (for example, using differential pressure sensors as in theapparatus 100A). At block 309 a, a water-liquid ratio (RWL) of themultiphase fluid 101 is determined (for example, using dynamic pressure sensors as in theapparatus 100E)). At block 311 a, a gas volume fraction (αg) is determined at least based on the densities of the various phases (determined at block 303 a), the mixture density (ρ) of the multiphase fluid 101 (determined at block 307 a), and the water-liquid ratio (RWL) of the multiphase fluid 101 (determined at block 309 a): ρ=(ρa×RWLρo×(1−RWL))×(1−αg)+ρg×αg. At block 313 a, a gas flow rate (Qg) of thegas phase 101 a is determined based on the gas volume fraction (αg) and the total volume flow rate (Q) of the multiphase fluid 101: Qg=αg×Q. At block 313 a, an aqueous phase flow rate (Qa) of theaqueous phase 101 b′ is determined based on the water-liquid ratio (RWL), the gas volume fraction (αg), and the overall flow rate (Q) of the multiphase fluid 101: Qa=RWL×(1−αg)×Q. At block 313 a, an oil phase flow rate (Qo) of theoil phase 101 b″ is determined based on the water-liquid ratio (RWL), the gas volume fraction (αg), and the total volume flow rate (Q) of the multiphase fluid 101: Qo=(1−RWL)×(1−αg)×Q. -
FIG. 3B is a flowchart depicting an example multiphasefluid flow model 300B. Any one of theapparatuses model 300B to characterize a multiphase fluid, such as themultiphase fluid 101. Atblock 301 b, a first differential pressure (ΔP1) and a second differential pressure (ΔP2) of the flowingmultiphase fluid 101 is measured. The first differential pressure (ΔP1) is measured in a first direction across a specified differential pressure height (h). The second differential pressure (ΔP2) is measured in a second direction (different from the first direction) across the specified differential pressure height (h). The first and second directions are such that themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction. For example, themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction. For example, themultiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction. - At
block 303 b, a frictional pressure loss (ΔPf) of the flowingmultiphase fluid 101 is calculated based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 b. The frictional pressure loss (ΔPf) can be calculated atblock 303 b, for example, by Equation 2h. Atblock 305 b, a mixture density (ρ) of themultiphase fluid 101 is calculated based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 b. The mixture density (ρ) can be calculated atblock 305 b, for example, by Equation 2d. Atblock 307 b, a gas phase volume fraction (αg) of themultiphase fluid 101 is calculated based on the mixture density (ρ) determined atblock 305 b. The gas phase volume fraction (αg) can be calculated atblock 307 b, for example, by Equation 3b. In some implementations, gas phase volume fraction (αg) can be calculated atblock 307 b based on other known or measured parameters, such as density of the liquid phase (ρl) and density of the gas phase (ρg). In such implementations, the gas phase volume fraction (αg) can be calculated by Equation 6a. -
- In some implementations, a total mass flow rate (mT) of the
multiphase fluid 101 is determined. The total mass flow rate (mT) can be determined, for example, by a mass flowmeter and/or by any of Equations 3a, 4a, or 4b. The multiphasefluid flow model 300B assumes that a slip ratio (S) of themultiphase fluid 101 is substantially equal to 1. The slip ratio (S) is the ratio of the velocity of the gas phase to the velocity of the liquid phase (including the aqueous phase and the oil phase) in the flowingmultiphase fluid 101. -
FIG. 3C is a flowchart depicting an example multiphasefluid flow model 300C. Any one of theapparatuses model 300C to characterize a multiphase fluid, such as themultiphase fluid 101. Atblock 301 c, a first differential pressure (ΔP1) and a second differential pressure (ΔP2) of the flowingmultiphase fluid 101 is measured. The first differential pressure (ΔP1) is measured in a first direction across a specified differential pressure height (h). The second differential pressure (ΔP2) is measured in a second direction (different from the first direction) across the specified differential pressure height (h). The first and second directions are such that themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction. For example, themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction. For example, themultiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction. - At
block 303 c, a frictional pressure loss (ΔPf) of the flowingmultiphase fluid 101 is calculated based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 c. The frictional pressure loss (ΔPf) can be calculated atblock 303 c, for example, by Equation 2h. Atblock 305 c, an apparent mixture density (ρapp) of themultiphase fluid 101 is estimated based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 c. The apparent mixture density (ρapp) can be estimated atblock 305 c, for example, by Equation 2d. Atblock 307 c, a void fraction (λg) of themultiphase fluid 101 is calculated based on the apparent mixture density (ρapp) estimated atblock 305 c. The void fraction (λg) can be calculated atblock 307 c, for example, by Equation 6b. -
- At
block 309 c, various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowingmultiphase fluid 101 are determined. The conditions and/or properties determined atblock 309 c can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). Atblock 311 c, a water-liquid ratio (RWL) of the flowingmultiphase fluid 101 is determined. The water-liquid ratio (RWL) can be determined atblock 311 c can be measured, for example, by external sensors (such as dynamic pressure sensors, as inapparatus 100G shown inFIG. 1G ). Atblock 313 c, densities of the various phases (such as density of the gas phase (ρg), density of the aqueous phase (ρa), and density of the oil phase (ρo)) of the flowingmultiphase fluid 101 are determined. The densities of the various phases of the flowingmultiphase fluid 101 can be determined atblock 313 c, for example, based on the operating conditions (pressure and temperature) of the flowingmultiphase fluid 101 determined atblock 309 c. Atblock 313 c, a density of the liquid phase (ρl, including the aqueous phase and the oil phase) is determined. The density of the liquid phase (ρl) can be determined atblock 313 c based on the densities of the various phases of the flowingmultiphase fluid 101 and the water-liquid ratio (RWL) determined atblock 311 c. The density of the liquid phase (ρl) can be determined atblock 313 c by Equation 6c. -
βl=ρa R WL+πo(1−R WL) (6c) - In some implementations, the void fraction (λg) can be calculated at
block 307 c based on the density of the liquid phase (ρl) and the density of the gas phase (ρg) determined atblock 313 c. - At
block 315 c, a gas phase volume fraction (αg) of themultiphase fluid 101 is calculated based on the void fraction (λg) determined atblock 307 c and slip ratio (S) of the flowingmultiphase fluid 101. The slip ratio (S) used atblock 315 c to determine the gas phase volume fraction (αg) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess. Atblock 317 c, a mixture density (ρ) of themultiphase fluid 101 is calculated based on the gas phase volume fraction (αg) determined atblock 315 c, the density of the gas phase (ρg) determined atblock 313 c, and the density of the liquid phase (ρl) determined atblock 313 c. The mixture density (ρ) can be determined atblock 317 c by Equation 6d. -
ρ=αgρg+(1−αg)ρl (6d) - In some implementations, a total mass flow rate (mT) of the
multiphase fluid 101 is determined. The total mass flow rate (mT) can be determined, for example, by a mass flowmeter and/or by any of Equations 3a, 4a, or 4b. In some implementations, the blocks in the dotted box of the multiphasefluid flow model 300C (blocks fluid flow model 300C (blocks -
FIG. 3D is a flowchart depicting an example multiphasefluid flow model 300D. Any one of theapparatuses model 300D to characterize a multiphase fluid, such as themultiphase fluid 101. Atblock 301 d, a first differential pressure (ΔP1) and a second differential pressure (ΔP2) of the flowingmultiphase fluid 101 is measured. The first differential pressure (ΔP1) is measured in a first direction across a specified differential pressure height (h). The second differential pressure (ΔP2) is measured in a second direction (different from the first direction) across the specified differential pressure height (h). The first and second directions are such that themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction. For example, themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction. For example, themultiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction. - At
block 303 d, a frictional pressure loss (ΔPf) of the flowingmultiphase fluid 101 is calculated based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 d. The frictional pressure loss (ΔPf) can be calculated atblock 303 d, for example, by Equation 2h. Atblock 305 d, an apparent mixture density (ρapp) of themultiphase fluid 101 is estimated based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 d. The apparent mixture density (ρapp) can be estimated atblock 305 d, for example, by Equation 2d. - At
block 307 d, various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowingmultiphase fluid 101 are determined. The conditions and/or properties determined atblock 307 d can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). Atblock 309 d, densities of the various phases (such as density of the gas phase (ρg), density of the aqueous phase (ρa), and density of the oil phase (ρo)) of the flowingmultiphase fluid 101 are determined. The densities of the various phases of the flowingmultiphase fluid 101 can be determined atblock 309 d, for example, based on the operating conditions (pressure and temperature) of the flowingmultiphase fluid 101 determined atblock 307 d. Atblock 311 d, a gas phase volume fraction (αg) of the flowingmultiphase fluid 101 is determined. The gas phase volume fraction (αg) determined atblock 311 d can be measured, for example, by an external sensor (such as an ultrasonic sensor). - At
block 313 d, a void fraction (λg) of themultiphase fluid 101 is calculated based on the gas volume fraction fraction (αg) determined atblock 311 d and slip ratio (S) of the flowingmultiphase fluid 101. The slip ratio (S) used atblock 313 d to determine the void fraction (λg) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess. Atblock 315 d, a density of the liquid phase (ρl, including the aqueous phase and the oil phase) is determined. The density of the liquid phase (ρl) can be determined atblock 315 d based on the apparent mixture density (ρapp) determined atblock 305 d, the densities of the various phases of the flowingmultiphase fluid 101 determined atblock 309 d, and the void fraction (λg) determined atblock 313 d. The density of the liquid phase (ρl) can be calculated atblock 315 d, for example, by Equation 6e. -
- At
block 317 d, a mixture density (ρ) of themultiphase fluid 101 is calculated based on the density of the gas phase (ρg) determined atblock 309 d, the gas phase volume fraction (αg) determined atblock 311 d, and the density of the liquid phase (ρl) determined atblock 315 d. The mixture density (ρ) can be determined atblock 317 c by Equation 6d. - In some implementations, a total mass flow rate (mT) of the
multiphase fluid 101 is determined. The total mass flow rate (mT) can be determined, for example, by a mass flowmeter and/or by any of Equations 3a, 4a, or 4b. In some implementations, the blocks in the dotted box of the multiphasefluid flow model 300D (blocks 313 d, 315 d, 317 d, determining the total mass flow rate (mT), and determining the slip ratio (S)) are performed simultaneously (for example, in parallel). In some implementations, the blocks in the dotted box of the multiphasefluid flow model 300D (blocks 313 d, 315 d, 317 d, determining the total mass flow rate (mT), and determining the slip ratio (S)) are performed iteratively (for example, in series) until the calculated values converge to final values. Atblock 319 d, a water-liquid ratio (RWL) of themultiphase fluid 101 is determined. The water-liquid ratio (RWL) can be determined atblock 319 d by re-arranging Equation 6c to solve for RWL -
-
FIG. 3E is a flowchart depicting an example multiphasefluid flow model 300E. Any one of theapparatuses model 300E to characterize a multiphase fluid, such as themultiphase fluid 101. Atblock 301 e, a first differential pressure (ΔP1) and a second differential pressure (ΔP2) of the flowingmultiphase fluid 101 is measured. The first differential pressure (ΔP1) is measured across a first bend in piping. The second differential pressure (ΔP2) is measured across a second bend in piping. Themultiphase fluid 101 flows generally upward across either of the first or second bends and flows generally downward across the other of the first or second bends. For example, themultiphase fluid 101 flows generally upward across the first bend and flows generally downward across the second bend. For example, themultiphase fluid 101 flows generally downward across the first bend and flows generally upward across the second bend. Examples are provided with respect toapparatuses FIGS. 1E, 1F, 1H, 1I, and 1J , respectively). Atblock 303 e, either one of the first differential pressure (ΔP1) or the second differential pressure (ΔP2) measured atblock 301 e is selected for further calculations in themodel 300E. - At
block 305e, a void fraction (λg) of themultiphase fluid 101 is determined. The void fraction (λg) determined atblock 305 e can be measured for example, by an external sensor (such as an ultrasonic sensor). Atblock 307 e, various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowingmultiphase fluid 101 are determined. The conditions and/or properties determined atblock 307 e can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). Atblock 309 e, a water-liquid ratio (RWL) of the flowingmultiphase fluid 101 is determined. The water-liquid ratio (RWL) can be determined atblock 309 e can be measured, for example, by external sensors (such as dynamic pressure sensors, as inapparatus 100G shown inFIG. 1G ). Atblock 311 e, densities of the various phases (such as density of the gas phase (ρg), density of the aqueous phase (ρa), and density of the oil phase (ρo)) of the flowingmultiphase fluid 101 are determined. The densities of the various phases of the flowingmultiphase fluid 101 can be determined atblock 311 e, for example, based on the operating conditions (pressure and temperature) of the flowingmultiphase fluid 101 determined atblock 307 e. Atblock 311 e, a density of the liquid phase (ρl, including the aqueous phase and the oil phase) is determined. The density of the liquid phase (ρl) can be determined atblock 311 e based on the densities of the various phases of the flowingmultiphase fluid 101 and the water-liquid ratio (RWL) determined atblock 309 e. The density of the liquid phase (ρl) can be determined atblock 311 e by Equation 6c. In some implementations, the void fraction (λg) can be calculated atblock 305 e based on the density of the liquid phase (ρl) and the density of the gas phase (ρg) determined atblock 311 e. - At
block 313 e, a gas phase volume fraction (αg) of themultiphase fluid 101 is calculated based on the void fraction (λg) determined atblock 305 e and slip ratio (S) of the flowingmultiphase fluid 101. The slip ratio (S) used atblock 313 e to determine the gas phase volume fraction (αg) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess. Atblock 315 e, a mixture density (ρ) of themultiphase fluid 101 is calculated based on the gas phase volume fraction (αg) determined atblock 313 e, the density of the gas phase (ρg) determined atblock 311 e, and the density of the liquid phase (ρl) determined atblock 311 e. The mixture density (ρ) can be determined atblock 315 e by Equation 6d. Atblock 317 e, a total mass flow rate (mT) of themultiphase fluid 101 is determined. The total mass flow rate (mT) can be determined atblock 317 e, for example, by a mass flowmeter and/or by any of Equations 4a or 4b based on the selected differential pressure atblock 303 e. In some implementations, the blocks in the dotted box of the multiphasefluid flow model 300E (blocks 313 e, 315 e, 317 e, and determining the slip ratio (S)) are performed simultaneously (for example, in parallel). In some implementations, the blocks in the dotted box of the multiphasefluid flow model 300E (blocks 313 e, 315 e, 317 e, and determining the slip ratio (S)) are performed iteratively (for example, in series) until the calculated values converge to final values. -
FIG. 3F is a flowchart depicting an example multiphasefluid flow model 300F. Any one of theapparatuses model 300F to characterize a multiphase fluid, such as themultiphase fluid 101. Atblock 301 f, a first differential pressure (ΔP1) and a second differential pressure (ΔP2) of the flowingmultiphase fluid 101 is measured. The first differential pressure (ΔP1) is measured across a first bend in piping. The second differential pressure (ΔP2) is measured across a second bend in piping. Themultiphase fluid 101 flows generally upward across either of the first or second bends and flows generally downward across the other of the first or second bends. For example, themultiphase fluid 101 flows generally upward across the first bend and flows generally downward across the second bend. For example, themultiphase fluid 101 flows generally downward across the first bend and flows generally upward across the second bend. Examples are provided with respect toapparatuses FIGS. 1E, 1F, 1H, 1I, and 1J , respectively). - At
block 303 f, a third differential pressure (ΔP3) and a fourth differential pressure (ΔP4) of the flowingmultiphase fluid 101 is measured. The third differential pressure (ΔP1) is measured in a first direction across a specified differential pressure height (h). The second differential pressure (ΔP2) is measured in a second direction (different from the first direction) across the specified differential pressure height (h). The first and second directions are such that themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in one of the first or second directions and flows generally downward across the specified differential pressure height (h) in the other direction. For example, themultiphase fluid 101 flows generally upward across the specified differential pressure height (h) in the first direction and flows generally downward across the specified differential pressure height (h) in the second direction. For example, themultiphase fluid 101 flows generally downward across the specified differential pressure height (h) in the first direction and flows generally upward across the specified differential pressure height (h) in the second direction. - At
block 305 f, a frictional pressure loss (ΔPf) of the flowingmultiphase fluid 101 is calculated based on the third and fourth differential pressures (ΔP3, ΔP4) measured atblock 303 f. The frictional pressure loss (ΔPf) can be calculated atblock 305 f, for example, by Equation 2h. Atblock 307 f, an apparent mixture density (ρapp) of themultiphase fluid 101 is estimated based on the third and fourth differential pressures (ΔP3, ΔP4) measured atblock 303 f. The apparent mixture density (ρapp) can be estimated atblock 307 f, for example, by Equation 2d. Atblock 309 f, a void fraction (λg) of themultiphase fluid 101 is calculated based on the apparent mixture density (ρapp) estimated atblock 307 f. The void fraction (λg) can be calculated atblock 309 f, for example, by Equation 6b. - At
block 311 f, various operating conditions and/or properties (such as pressure, temperature, and salinity) about the flowingmultiphase fluid 101 are determined. The conditions and/or properties determined atblock 311 f can be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). Atblock 313 f, a water-liquid ratio (RWL) of the flowingmultiphase fluid 101 is determined. The water-liquid ratio (RWL) can be determined atblock 313 f can be measured, for example, by external sensors (such as dynamic pressure sensors, as inapparatus 100G shown inFIG. 1G ). Atblock 315 f, densities of the various phases (such as density of the gas phase (ρg), density of the aqueous phase (ρa), and density of the oil phase (ρo)) of the flowingmultiphase fluid 101 are determined. The densities of the various phases of the flowingmultiphase fluid 101 can be determined atblock 315 f, for example, based on the operating conditions (pressure and temperature) of the flowingmultiphase fluid 101 determined atblock 311 f. Atblock 315 f, a density of the liquid phase (ρl, including the aqueous phase and the oil phase) is determined. The density of the liquid phase (ρl) can be determined atblock 315 f based on the densities of the various phases of the flowingmultiphase fluid 101 and the water-liquid ratio (RWL) determined atblock 313 f. The density of the liquid phase (ρl) can be determined atblock 315 f by Equation 6c. In some implementations, the void fraction (λg) can be calculated atblock 309 f based on the density of the liquid phase (ρl) and the density of the gas phase (ρg) determined atblock 315 f. - At
block 317 f, a gas phase volume fraction (αg) of themultiphase fluid 101 is calculated based on the void fraction (λg) determined atblock 309 f and slip ratio (S) of the flowingmultiphase fluid 101. The slip ratio (S) used atblock 317 f to determine the gas phase volume fraction (αg) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess. Atblock 319 f, a mixture density (ρ) of themultiphase fluid 101 is calculated based on the gas phase volume fraction (αg) determined atblock 317 f, the density of the gas phase (ρg) determined atblock 315 f, and the density of the liquid phase (ρl) determined atblock 315 f. The mixture density (ρ) can be determined atblock 319 f by Equation 6d. - At
block 321 f, a friction factor (fd) of the flowingmultiphase fluid 101 is determined based on the frictional pressure loss (ΔPf) determined atblock 305 f. Atblock 323 f, a horizontal flow dynamic pressure (qh) and a vertical flow dynamic pressure (qv) are determined. The horizontal flow dynamic pressure (qh) and the vertical flow dynamic pressure (qv) determined atblock 323 f can be, for example, measured by external sensors (such as dynamic pressure sensors). In some implementations, the horizontal flow dynamic pressure (qh) is determined by Equation 6fh. In some implementations, the vertical flow dynamic pressure (qv) is determined by Equation 6fv. In some implementations, the friction factor (fd) is determined atblock 321 f by Equation 6g, which depends on the horizontal flow dynamic pressure (qh) and the vertical flow dynamic pressure (qv) determined atblock 323 f (for example, by sensors or by Equations 6fh and 6fv. -
- In Equation 6fh, Ah is a cross-sectional flow area for the horizontal flow of the
multiphase fluid 101. In Equation 6fv, Av is a cross-sectional flow area for the vertical flow of themultiphase fluid 101. In Equation 6g, h is the specified differential pressure height, and Dv is the inner diameter of the conduit in which the direction of flow of themultiphase fluid 101 is generally upward or generally downward. - At block 325 f, a total mass flow rate (mT) of the
multiphase fluid 101 is determined. The total mass flow rate (mT) can be determined at block 325 f, for example, by a mass flowmeter and/or by any of Equations 4a or 4b. The total mass flow rate (mT) can be determined at block 325 f based on the first and second differential pressures (ΔP1, ΔP2) measured atblock 301 f, the mixture density (ρ) determined atblock 319 f, the friction factor (fd) determined atblock 321 f, and the horizontal and vertical flow dynamic pressures (qh, qv) determined atblock 323 f. In some implementations, the total mass flow rate (mT) is determined at block 325 f by Equation 6h. -
- where Cd is an empirically characterized discharge coefficient, ε is an expansion factor, K is a fixed geometry factor (K=A/√{square root over (1−β4)}, where A is the cross-sectional flow area of the throat of the bend and β is the beta ratio (d/D, where d is the inner diameter downstream of the bend and D is the inner diameter upstream of the bend)), ΔPL, is the differential pressure across the bend (selected from one of the first or second differential pressures (ΔP1 or ΔP2)), g is the acceleration due to gravity, y is the vertical height difference between the pressure ports for the differential pressure sensor, x is the horizontal distance between the pressure ports for the differential pressure sensor, D′h is the equivalent (effective) inner diameter of the cross-sectional flow area for the horizontal flow of the
multiphase fluid 101, and D′v is the equivalent (effective) inner diameter of the cross-sectional flow area for the vertical flow of themultiphase fluid 101. - In some implementations, the blocks in the dotted box of the multiphase
fluid flow model 300F (blocks fluid flow model 300F (blocks multiphase fluid 101 are determined. The various volumetric flow rates determined at block 327 f can include a total volumetric flow rate (QT) of themultiphase fluid 101, a gas phase volumetric flow rate (Qg) of themultiphase fluid 101, a liquid phase volumetric flow rate (Ql, including the aqueous phase and the oil phase) of themultiphase fluid 101, an oil phase volumetric flow rate (Qo) of themultiphase fluid 101, and an aqueous phase volumetric flow rate (Qa) of themultiphase fluid 101. The various volumetric flow rates determined at block 327 f can be calculated by Equations 6jt, 6jg, 6jl, 6jo, and 6ja. -
-
FIG. 3G is a flowchart depicting an example multiphasefluid flow model 300G. Any one of theapparatuses model 300G to characterize a multiphase fluid, such as themultiphase fluid 101. Atblock 301 g, various operating conditions (such as pressure and temperature) about the flowingmultiphase fluid 101 are determined. The various operating conditions determined atblock 301 g can be measured, for example, by external sensors, such as pressure sensors and temperature sensors. The various operating conditions determined atblock 301 g can include, for example, differential pressure measurements. Atblock 303 g, a salinity of the aqueous phase of themultiphase fluid 101 is measured. The salinity of the aqueous phase of themultiphase fluid 101 can be measured atblock 303 g, for example, using a salinity sensor. In some implementations, the salinity sensor includes electrodes for generating a current to measure conductivity of the aqueous phase of themultiphase fluid 101. Atblock 305 g, fluid properties (such as density) of the various phases (such as the gas phase, the aqueous phase, and the oil phase) of themultiphase fluid 101 are determined. The fluid properties of the various phases can be determined atblock 305 g based on the operating conditions measured atblock 301 g and the salinity of the aqueous phase measured atblock 303 g. Atblock 307 g, a void fraction (λg) of themultiphase fluid 101 is determined. The void fraction (λg) can be determined atblock 307 g, for example, using an external sensor (such as an ultrasonic sensor) and/or by Equation 6b. Atblock 309 g, a water-liquid ratio (RWL) of themultiphase fluid 101 is determined. The water-liquid ratio (RWL) can be determined atblock 309 g, for example, using an external sensor (such as a dynamic pressure sensor). Atblock 311 g, a density of the liquid phase (ρl, including the aqueous phase and the oil phase) is determined. The density of the liquid phase (ρl) can be determined atblock 311 g based on the densities of the various phases of the flowingmultiphase fluid 101 and the water-liquid ratio (RWL) determined atblock 309 g. The density of the liquid phase (ρl) can be determined atblock 311 g, for example, by Equation 6c. - At
block 313 g, a gas phase volume fraction (αg) of themultiphase fluid 101 is calculated based on the void fraction (λg) determined atblock 307 g and slip ratio (S) of the flowingmultiphase fluid 101. The slip ratio (S) used atblock 313 g to determine the gas phase volume fraction (αg) can, for example, be measured by an external sensor or assumed to be substantially equal to 1 as an initial guess. Atblock 315 g, a mixture density (ρ) of themultiphase fluid 101 is calculated based on the gas phase volume fraction (αg) determined atblock 313 g, the density of the gas phase (ρg) determined atblock 305 g, and the density of the liquid phase (ρl) determined atblock 311 g. The mixture density (ρ) can be determined atblock 315 g, for example, by Equation 6d. Atblock 317 g, a total mass flow rate (mT) of themultiphase fluid 101 is determined. The total mass flow rate (mT) can be determined atblock 317 g, for example, by a mass flowmeter and/or by any of Equations 4a or 4b. In some implementations, the blocks in the dotted box of the multiphasefluid flow model 300G (blocks fluid flow model 300G (blocks - At
block 319 g, various volumetric flow rates of themultiphase fluid 101 are determined. The various volumetric flow rates determined atblock 319 g can include a total volumetric flow rate (QT) of themultiphase fluid 101, a gas phase volumetric flow rate (Qg) of themultiphase fluid 101, a liquid phase volumetric flow rate (Ql, including the aqueous phase and the oil phase) of themultiphase fluid 101, an oil phase volumetric flow rate (Qo) of themultiphase fluid 101, and an aqueous phase volumetric flow rate (Qa) of themultiphase fluid 101. The various volumetric flow rates determined atblock 319 g can be calculated by Equations 6jt, 6jg, 6jl, 6jo, and 6ja. -
FIG. 4 is a flowchart of anexample method 400 for measuring a density of amultiphase fluid 101. Any one of theapparatuses method 400. Atblock 402, a multiphase fluid (such as the multiphase fluid 101) is flowed through a U-bend (such as the U-bend 102). Themultiphase fluid 101 can include agas phase 101 a, anaqueous phase 101 b′, and anoil phase 101 b″. As described previously, the U-bend 102 includes afirst conduit 102 a, asecond conduit 102 b, and a connectingconduit 102 c. Thefirst conduit 102 a is parallel to thesecond conduit 102 b. The connectingconduit 102 c connects thesecond conduit 102 b to thefirst conduit 102 a. Each of thefirst conduit 102 a, thesecond conduit 102 b, and the connectingconduit 102 c have substantially the same cross-sectional flow area for themultiphase fluid 101 flowing through the U-bend 102. Themultiphase fluid 101 flowing through the U-bend 102 flows into thefirst conduit 102 a, through the connectingconduit 102 c, and out of thesecond conduit 102 b. Atblock 404, a first differential pressure (ΔP1) of themultiphase fluid 101 is measured across a specified differential pressure height (h) along thefirst conduit 102 a. The first differential pressure (ΔP1) of themultiphase fluid 101 can be measured atblock 404, for example, by the first pair ofpressure sensors multiphase fluid 101 is measured across the specified differential pressure height (h) along thesecond conduit 102 b. The second differential pressure (ΔP2) of themultiphase fluid 101 can be measured at block 406, for example, by the second pair ofpressure sensors block 408, a mixture density (ρ) of themultiphase fluid 101 is determined at least based on a difference between the first differential pressure (ΔP1) and the second differential pressure (ΔP2) of the multiphase fluid 101 (measured atblocks 404 and 406, respectively) and the specified differential pressure height (h). For example, the mixture density (ρ) of themultiphase fluid 101 can be determined at block 406 using Equation 2d. - In some implementations, the
method 400 includes determining an aqueous phase volume fraction (αa) of themultiphase fluid 101 at least based on the gas phase volume fraction (αg) of themultiphase fluid 101, the gas density (ρg) of thegas phase 101 a of themultiphase fluid 101, the aqueous phase density (ρa) of theaqueous phase 101 b′ of themultiphase fluid 101, the oil phase density (ρo) of theoil phase 101 b″ of themultiphase fluid 101, and the mixture density (ρ) of themultiphase fluid 101. For example, the gas phase volume fraction (αg), the gas density (ρg), the aqueous phase density (ρa), the oil phase density (ρo), and the mixture density (ρ) of themultiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the aqueous phase volume fraction (αa) of themultiphase fluid 101. - In some implementations, the
method 400 includes determining a gas phase volume fraction (αg) of themultiphase fluid 101 at least based on the aqueous phase volume fraction (αa) of themultiphase fluid 101, the gas density (ρg) of thegas phase 101 a of themultiphase fluid 101, the aqueous phase density (ρa) of theaqueous phase 101 b′ of themultiphase fluid 101, the oil phase density (ρo) of theoil phase 101 b″ of themultiphase fluid 101, and the mixture density (ρ) of themultiphase fluid 101. For example, the aqueous phase volume fraction (αa), the gas density (ρg), the aqueous phase density (ρa), the oil phase density (ρo), and the mixture density (ρ) of themultiphase fluid 101 can be input to Equation 3b and re-arranged to calculate the gas phase volume fraction (αg) of themultiphase fluid 101. -
FIG. 5 is a flowchart of anexample method 500 for measuring a total flow rate of amultiphase fluid 101. Any one of theapparatuses method 500. Atblock 502, a multiphase fluid (such as the multiphase fluid 101) is flowed from a flow pipe (such as the flow pipe 150) to a U-bend (such as the U-bend 102). Themultiphase fluid 101 can include agas phase 101 a, anaqueous phase 101 b′, and anoil phase 101 b″. As described previously, the U-bend 102 includes afirst conduit 102 a, asecond conduit 102 b, and a connectingconduit 102 c. The connectingconduit 102 c connects thefirst conduit 102 a to thesecond conduit 102 b. Themultiphase fluid 101 flowing through the U-bend 102 flows into thefirst conduit 102 a, through the connectingconduit 102 c, and out of thesecond conduit 102 b. Theflow pipe 150 includes thefirst pipe 150 a (third conduit) and thesecond pipe 150 b (fourth conduit). Thefirst pipe 150 a is connected to thefirst conduit 102 a of the U-bend 102 by a first bend (such as the firstangled bend 153 a). Thesecond pipe 150 b is connected to thesecond conduit 102 b of the U-bend 102 by a second bend (such as the secondangled bend 153 b). Flowing themultiphase fluid 101 from theflow pipe 150 to the U-bend 102 atblock 502 includes flowing themultiphase fluid 101 from thefirst pipe 150 a of theflow pipe 150 through the firstangled bend 153 a to thefirst conduit 102 a of the U-bend 102. Atblock 504, themultiphase fluid 101 is flowed from the U-bend 102 to theflow pipe 150. Flowing themultiphase fluid 101 from the U-bend 102 to theflow pipe 150 atblock 504 includes flowing themultiphase fluid 101 from thesecond conduit 102 b of the U-bend 102 through the secondangled bend 153 b to thesecond pipe 150 b of theflow pipe 150. Atblock 506, a first differential pressure of themultiphase fluid 101 is measured between a first location on thefirst pipe 150 a of theflow pipe 150 and a second location on thefirst conduit 102 a of the U-bend 102. For example, the first differential pressure of themultiphase fluid 101 can be measured atblock 506 cooperatively by thefirst pressure sensor 104 a coupled to thefirst pipe 150 a of theflow pipe 150 at the first location and by thesecond pressure sensor 104 b coupled to thefirst conduit 102 a of the U-bend at the second location. Atblock 508, a second differential pressure of themultiphase fluid 101 is measured between a third location on thesecond conduit 102 b of the U-bend 102 and a fourth location on thesecond pipe 150 b of theflow pipe 150. The second differential pressure of themultiphase fluid 101 can be measured atblock 508 cooperatively by thethird pressure sensor 104 c coupled to thesecond conduit 102 b of the U-bend 102 at the third location and by thefourth pressure sensor 104 d coupled to thesecond pipe 150 b of theflow pipe 150 at the fourth location. Atblock 510, an overall flow rate of themultiphase fluid 101 is determined at least based on the first differential pressure (measured at block 506), the second differential pressure (measured at block 508), a difference between the first differential pressure and the second differential pressure, and an overall density of themultiphase fluid 101. For example, the total mass flow rate (mT1) of themultiphase fluid 101 can be determined atblock 510 using Equation 4a. For example, the total mass flow rate (mT2) of themultiphase fluid 101 can be determined atblock 510 using Equation 4b. In some implementations, themethod 500 includes comparing the total flow rates (mT1, mT2) of themultiphase fluid 101 determined at block 510 (for example, determined by Equations 4a and 4b) to determine an adjustment of the discharge coefficients (for example, Cd1, Cd2). -
FIG. 6 is a flowchart of anexample method 600 for measuring a mixture density, a total flow rate, and phase flow rates of amultiphase fluid 101. Any of theapparatuses method 600. Atblock 602, a multiphase fluid (such as the multiphase fluid 101) is flowed from a flow pipe (such as the flow pipe 150) to a U-bend (such as the U-bend 102). Themultiphase fluid 101 can include agas phase 101 a, anaqueous phase 101 b′, and anoil phase 101 b″. As described previously, the U-bend 102 includes afirst conduit 102 a, asecond conduit 102 b, and a connectingconduit 102 c. The connectingconduit 102 c connects thefirst conduit 102 a to thesecond conduit 102 b. Themultiphase fluid 101 flowing through the U-bend 102 flows into thefirst conduit 102 a, through the connectingconduit 102 c, and out of thesecond conduit 102 b. Theflow pipe 150 includes thefirst pipe 150 a (third conduit) and thesecond pipe 150 b (fourth conduit). Thefirst pipe 150 a is connected to thefirst conduit 102 a of the U-bend 102 by a first bend (such as the firstangled bend 153 a). Thesecond pipe 150 b is connected to thesecond conduit 102 b of the U-bend 102 by a second bend (such as the secondangled bend 153 b). Flowing themultiphase fluid 101 from theflow pipe 150 to the U-bend 102 atblock 602 includes flowing themultiphase fluid 101 from thefirst pipe 150 a of theflow pipe 150 through the firstangled bend 153 a to thefirst conduit 102 a of the U-bend 102. Atblock 604, themultiphase fluid 101 is flowed from the U-bend 102 to theflow pipe 150. Flowing themultiphase fluid 101 from the U-bend 102 to theflow pipe 150 atblock 604 includes flowing themultiphase fluid 101 from thesecond conduit 102 b of the U-bend 102 through the secondangled bend 153 b to thesecond pipe 150 b of theflow pipe 150. Atblock 606, a first differential pressure of themultiphase fluid 101 is measured between a first location on thefirst pipe 150 a of theflow pipe 150 and a second location on thefirst conduit 102 a of the U-bend 102. For example, the first differential pressure of themultiphase fluid 101 can be measured atblock 606 cooperatively by thefirst pressure sensor 104 a coupled to thefirst pipe 150 a of theflow pipe 150 at the first location and by thesecond pressure sensor 104 b coupled to thefirst conduit 102 a of the U-bend at the second location. Atblock 608, a second differential pressure of themultiphase fluid 101 is measured between a third location on thesecond conduit 102 b of the U-bend 102 and a fourth location on thesecond pipe 150 b of theflow pipe 150. The second differential pressure of themultiphase fluid 101 can be measured atblock 608 cooperatively by thethird pressure sensor 104 c coupled to thesecond conduit 102 b of the U-bend 102 at the third location and by thefourth pressure sensor 104 d coupled to thesecond pipe 150 b of theflow pipe 150 at the fourth location. Atblock 610, a third differential pressure of themultiphase fluid 101 is measured across a specified height (such as the specified height, h) along the longitudinal length of thefirst conduit 102 a of the U-bend 102. The third differential pressure of themultiphase fluid 101 can be measured atblock 610 by the third pair ofpressure sensors first conduit 102 a. Atblock 612, a fourth differential pressure of themultiphase fluid 101 is measured across the specified height (h) along the longitudinal length of thesecond conduit 102 b of the U-bend 102. The fourth differential pressure of themultiphase fluid 101 can be measured atblock 612 by the fourth pair ofpressure sensors 104 g, 104 h coupled to thesecond conduit 102 b. Atblock 614, a mixture density (ρ) of themultiphase fluid 101 is determined at least based on a difference between the third differential pressure (ΔP3) and the fourth differential pressure (ΔP4) of the multiphase fluid 101 (measured atblocks multiphase fluid 101 can be determined atblock 614 using Equation 2d, where ΔP1 is substituted for the third differential pressure (ΔP3) measured by the third pair ofpressure sensors block 610, ΔP2 is substituted for the fourth differential pressure (ΔP4) measured by the fourth pair ofpressure sensors 104 g, 104 h atblock 612, and h2 is substituted for the specified height (h). Atblock 616, a total flow rate of themultiphase fluid 101 is determined at least based on the first differential pressure (measured at block 606), the second differential pressure (measured at block 608), and a mixture density of the multiphase fluid 101 (determined at block 614). For example, the total mass flow rate (mT1) of themultiphase fluid 101 can be determined atblock 616 using Equation 4a. For example, the total mass flow rate (mT2) of themultiphase fluid 101 can be determined atblock 616 using Equation 4b. - In some implementations, the
method 600 includes comparing the total flow rates (mT1, mT2) of themultiphase fluid 101 determined at block 616 (for example, determined by Equations 4a and 4b) to determine an adjustment of the discharge coefficients (Cd1, Cd2). In implementation in which themethod 600 is performed by theapparatus 100G, themethod 600 can include measuring various dynamic pressures of themultiphase fluid 101 flowing through the U-bend 102. The dynamic pressures of themultiphase fluid 101 can be measured, for example, by thedynamic pressure sensors dynamic pressure sensors multiphase fluid 101 flowing through the U-bend 102. The speed of sound of themultiphase fluid 101 and the mixture density (ρ) of themultiphase fluid 101 can then be used to determine the water-liquid ratio of themultiphase fluid 101. For example, the speed of sound of themultiphase fluid 101 and the mixture density (ρ) of themultiphase fluid 101 can be compared to a plotted graph of various phase curves (gas/oil, gas/aqueous, oil/aqueous) to determine the water-liquid ratio. -
FIG. 7 is a block diagram of anexample computer 700 used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures, as described in this specification, according to an implementation. The illustratedcomputer 700 is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, one or more processors within these devices, or any other processing device, including physical or virtual instances (or both) of the computing device. Additionally, thecomputer 700 can include a computer that includes an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of thecomputer 700, including digital data, visual, audio information, or a combination of information. - The
computer 700 includes aninterface 704. Although illustrated as asingle interface 704 inFIG. 7 , two ormore interfaces 704 may be used according to particular needs, desires, or particular implementations of thecomputer 700. Although not shown inFIG. 7 , thecomputer 700 can be communicably coupled with a network. Theinterface 704 is used by thecomputer 700 for communicating with other systems that are connected to the network in a distributed environment. Generally, theinterface 704 comprises logic encoded in software or hardware (or a combination of software and hardware) and is operable to communicate with the network. More specifically, theinterface 704 may comprise software supporting one or more communication protocols associated with communications such that the network or interface's hardware is operable to communicate physical signals within and outside of the illustratedcomputer 700. Theinterface 704 can include a control interface, which can be used to couple thecomputer 700 to controls. In some implementations, the control interface is a bank of relays, a bank of MOSFET power controllers, a serial peripheral interface (SPI), or a Fieldbus, and the like. Theinterface 704 can include a sensor interface, which can be used to couple thecomputer 700 to sensors. In some implementations, the sensor interface is a bank of analog-to-digital converters (ADCs), and I2C bus, a serial peripheral interface (SPI) bus, or a Fieldbus, and the like. Theinterface 704 can include a human machine interface, which can be used by a user to interact with thecomputer 700. In some implementations, the human machine interface includes a monitor or a touch screen that is configured to display information, for example, to a user. - The
computer 700 includes aprocessor 705. Theprocessor 705 may be a microprocessor, a multi-core processor, a multithreaded processor, an ultra-low-voltage processor, an embedded processor, or a virtual processor. In some embodiments, theprocessor 705 may be part of a system-on-a-chip (SoC) in which theprocessor 705 and the other components of thecomputer 700 are formed into a single integrated electronics package. In some implementations, theprocessor 705 may include processors from Intel® Corporation of Santa Clara, California, from Advanced Micro Devices, Inc. (AMD) of Sunnyvale, California, or from ARM Holdings, LTD., Of Cambridge, England. Any number of other processors from other suppliers may also be used. Although illustrated as asingle processor 705 inFIG. 7 , two or more processors may be used according to particular needs, desires, or particular implementations of thecomputer 700. Generally, theprocessor 705 executes instructions and manipulates data to perform the operations of thecomputer 700 and any algorithms, methods, functions, processes, flows, and procedures as described in this specification. Theprocessor 705 may communicate with other components of thecomputer 700 over a bus. The bus may include any number of technologies, such as industry standard architecture (ISA), extended ISA (EISA), peripheral component interconnect (PCI), peripheral component interconnect extended (PCIx), PCI express (PCIe), or any number of other technologies. The bus may be a proprietary bus, for example, used in an SoC based system. Other bus technologies may be used, in addition to, or instead of, the technologies above. - The
computer 700 can also include adatabase 706 that can hold data for thecomputer 700 or other components (or a combination of both) that can be connected to the network. Although illustrated as asingle database 706 inFIG. 7 , two or more databases (of the same or combination of types) can be used according to particular needs, desires, or particular implementations of thecomputer 700 and the described functionality. Whiledatabase 706 is illustrated as an integral component of thecomputer 700,database 706 can be external to thecomputer 700. Thedatabase 706 can be used for the persistent storage of information, such as data, applications, operating systems, and so forth. Thedatabase 706 may be a nonvolatile RAM, a solid-state disk drive, or a flash drive, among others. In some implementations, the database 306 will include a hard disk drive, such as a micro hard disk drive, a regular hard disk drive, or an array of hard disk drives, for example, associated with a DCS or a cloud server. - The
computer 700 also includes amemory 707 that can hold data for thecomputer 700 or other components (or a combination of both) that can be connected to the network. Although illustrated as asingle memory 707 inFIG. 7 , two or more memories 707 (of the same or combination of types) can be used according to particular needs, desires, or particular implementations of thecomputer 700 and the described functionality. Whilememory 707 is illustrated as an integral component of thecomputer 700,memory 707 can be external to thecomputer 700. Thememory 707 can be a transitory or non-transitory storage medium. In some implementations, such as in PLCs and other process control units, thememory 707 is integrated with thedatabase 706 used for long-term storage of programs and data. Thememory 707 can include any number of volatile and nonvolatile memory devices, such as volatile random-access memory (RAM), static random-access memory (SRAM), flash memory, and the like. In smaller devices, such as PLCs, thememory 707 may include registers associated with theprocessor 705 itself. - The
memory 707 stores computer-readable instructions executable by theprocessor 705 that, when executed, cause theprocessor 705 to perform operations, such as receiving a first differential pressure signal from the first pair ofpressure sensors pressure sensors multiphase fluid 101 at least based on a difference between the first differential pressure and the second differential pressure of themultiphase fluid 101 and the specified differential pressure height, h. Thecomputer 700 can also include apower supply 714. Thepower supply 714 can include a rechargeable or non-rechargeable battery that can be configured to be either user- or non-user-replaceable. Thepower supply 714 can be hard-wired. There may be any number ofcomputers 700 associated with, or external to, a computersystem containing computer 700, eachcomputer 700 communicating over the network. Further, the term “client,” “user,” “operator,” and other appropriate terminology may be used interchangeably, as appropriate, without departing from this specification. Moreover, this specification contemplates that many users may use onecomputer 700, or that one user may usemultiple computers 700. - While this specification contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular implementations. Certain features that are described in this specification in the context of separate implementations can also be implemented, in combination, in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations, separately, or in any sub-combination. Moreover, although previously described features may be described as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can, in some cases, be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.
- As used in this disclosure, the terms “a,” “an,” or “the” are used to include one or more than one unless the context clearly dictates otherwise. The term “or” is used to refer to a nonexclusive “or” unless otherwise indicated. The statement “at least one of A and B” has the same meaning as “A, B, or A and B.” In addition, it is to be understood that the phraseology or terminology employed in this disclosure, and not otherwise defined, is for the purpose of description only and not of limitation. Any use of section headings is intended to aid reading of the document and is not to be interpreted as limiting; information that is relevant to a section heading may occur within or outside of that particular section.
- As used in this disclosure, the term “about” or “approximately” can allow for a degree of variability in a value or range, for example, within 10%, within 5%, or within 1% of a stated value or of a stated limit of a range.
- As used in this disclosure, the term “substantially” refers to a majority of, or mostly, as in at least about 50%, 60%, 70%, 80%, 90%, 95%, 96%, 97%, 98%, 99%, 99.5%, 99.9%, 99.99%, or at least about 99.999% or more.
- Values expressed in a range format should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. For example, a range of “0.1% to about 5%” or “0.1% to 5%” should be interpreted to include about 0.1% to about 5%, as well as the individual values (for example, 1%, 2%, 3%, and 4%) and the sub-ranges (for example, 0.1% to 0.5%, 1.1% to 2.2%, 3.3% to 4.4%) within the indicated range. The statement “X to Y” has the same meaning as “about X to about Y,” unless indicated otherwise. Likewise, the statement “X, Y, or Z” has the same meaning as “about X, about Y, or about Z,” unless indicated otherwise.
- Particular implementations of the subject matter have been described. Other implementations, alterations, and permutations of the described implementations are within the scope of the following claims as will be apparent to those skilled in the art. While operations are depicted in the drawings or claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed (some operations may be considered optional), to achieve desirable results. In certain circumstances, multitasking or parallel processing (or a combination of multitasking and parallel processing) may be advantageous and performed as deemed appropriate.
- Moreover, the separation or integration of various system modules and components in the previously described implementations should not be understood as requiring such separation or integration in all implementations, and it should be understood that the described components and systems can generally be integrated together or packaged into multiple products.
- Accordingly, the previously described example implementations do not define or constrain the present disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of the present disclosure.
Claims (18)
m T =C d ×ε×K×√{square root over (2×ρ×(ΔP−k f ×ΔP f))},
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa),
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa),
m T =C d ×ε×K×√{square root over (2×ρ×(ΔP−k f ×ΔP f))},
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa),
ρ=ρg×αg+ρa×αa+ρo×(1−αg−αa),
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US20140012507A1 (en) * | 2012-07-09 | 2014-01-09 | Weatherford/Lamb, Inc. | In-well full-bore multiphase flowmeter for horizontal wellbores |
US20160341585A1 (en) * | 2015-05-19 | 2016-11-24 | Medeng Research Institute Ltd. | Multiphase Flow Meter |
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FR2720498B1 (en) * | 1994-05-27 | 1996-08-09 | Schlumberger Services Petrol | Multiphase flowmeter. |
NL1009248C2 (en) * | 1998-05-22 | 1999-11-24 | Groot Nijkerk Maschf B V De | Device for measuring the density of a flowing medium. |
US6807857B2 (en) * | 2002-06-05 | 2004-10-26 | Halliburton Energy Services, Inc. | Method and apparatus for determining density of a flowing fluid |
US20110296911A1 (en) * | 2010-06-02 | 2011-12-08 | Barry Moore | Method and apparatus for measuring the density of a flowing fluid in a conduit using differential pressure |
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2022
- 2022-07-19 US US17/868,545 patent/US20240027317A1/en active Pending
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US20020069022A1 (en) * | 1997-09-24 | 2002-06-06 | Fincke James R. | Multiphase flow calculation software |
US6622574B2 (en) * | 1997-09-24 | 2003-09-23 | Bechtel Bwxt Idaho, Llc | Oil field management system |
US20140012507A1 (en) * | 2012-07-09 | 2014-01-09 | Weatherford/Lamb, Inc. | In-well full-bore multiphase flowmeter for horizontal wellbores |
US20160341585A1 (en) * | 2015-05-19 | 2016-11-24 | Medeng Research Institute Ltd. | Multiphase Flow Meter |
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